How many questions are needed to find out the maximum of a Random Walk An introduction to probability theory and its application ,
Table of Integral, Series and Products, p.319, 1980. ,
A constant arising from the ano1ysis of algorithms for determining the maximum of a random walk, R.S.A, vol.10, pp.333-335, 1997. ,
Brownian Motion and Stochastic Calculus, 1988. ,
Some Complexity Results for Zero Finding for Univariate Functions, Journal of Complexity, vol.9, issue.1, pp.15-40, 1993. ,
DOI : 10.1006/jcom.1993.1003
Search for the maximum of a random walk, R.S.A, vol.6, pp.275-295, 1995. ,
Continuous Martingales and Brownian Motion, p.10, 1990. ,
Principes of Random Walk REFERENCES CHAPITRE II References The design and analysis of computer algorithm, pp.61-352, 1964. ,
The Average-Case Complexity of Determining the Majority, SIAM Journal on Computing, vol.26, issue.1, pp.1-14, 1997. ,
DOI : 10.1137/S0097539794275914
Applied probability and queues, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, 1987. ,
Optimal Search for a Maximum with Sequences of Simultaneous Function Evaluations, Management Science, vol.12, issue.9, pp.722-731, 1966. ,
DOI : 10.1287/mnsc.12.9.722
Elements of queuing theory. Palm-martingale calculus and stochastic recurrences, Applications of Mathematics, p.26, 1994. ,
Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions, preprint, 1999. ,
Valeurs principales associées aux temps locaux browniens, Bull. Sci. Maths, vol.111, pp.23-101, 1987. ,
Quelques précisions sur le méandre brownien, Bull. Sci. Maths, vol.112, pp.101-109, 1988. ,
Random Graphs, p.12, 1985. ,
On the laws of homogeneous functionals of the Brownian bridge, 1998. ,
Determining the majority: the biased case, The Annals of Applied Probability, vol.7, issue.2, pp.523-544, 1997. ,
DOI : 10.1214/aoap/1034625343
How many questions are needed to find out the maximum of a Random Walk, to appear in Stoch, Proc. and Applns, 1999. ,
Parking functions, empirical processes and the width of rooted labeled trees, 1999. ,
On the harmonie mean of depths of nodes of a random tree ,
Excursions in Brownian motion, Arkiv f??r Matematik, vol.14, issue.1-2, pp.155-177, 1976. ,
DOI : 10.1007/BF02385832
Average case selection, Journal of the ACM, vol.36, issue.2, pp.270-279, 1989. ,
DOI : 10.1145/62044.62047
A Random Walk and a Wiener Process Near a Maximum, Theory of Probability & Its Applications, vol.28, issue.4, pp.821-824, 1983. ,
DOI : 10.1137/1128082
Functionals of Brownian Meander and Brownian Excursion, The Annals of Probability, vol.5, issue.1, pp.130-135, 1977. ,
DOI : 10.1214/aop/1176995896
The Distribution of Heights of Binary Trees and Other Simple Trees, Combinatorics, Probability and Computing, vol.30, issue.02, pp.145-156, 1993. ,
DOI : 10.1016/0377-0427(91)90197-R
URL : https://hal.archives-ouvertes.fr/inria-00076989
The average height of binary trees and other simple trees, Journal of Computer and System Sciences, vol.25, issue.2, pp.171-213, 1982. ,
DOI : 10.1016/0022-0000(82)90004-6
URL : https://hal.archives-ouvertes.fr/inria-00076505
Euler Sums and Contour Integral Representations, Experimental Mathematics, vol.25, issue.1, pp.1-15, 1998. ,
DOI : 10.1016/0022-314X(87)90012-6
URL : https://hal.archives-ouvertes.fr/inria-00073780
On the Analysis of Linear Probing Hashing, Algorithmica, vol.22, issue.4, 1998. ,
DOI : 10.1007/PL00009236
URL : https://hal.archives-ouvertes.fr/inria-00073424
Asymptotic distribution theory for Hoare's selection algorithm, Advances in Applied Probability, vol.3, issue.01, pp.252-269, 1996. ,
DOI : 10.1016/0022-0000(84)90009-6
Locating the maximum of a simple random sequence by sequential search, IEEE Transactions on Information Theory, vol.33, issue.6, pp.877-88, 1987. ,
DOI : 10.1109/TIT.1987.1057378
A constant arising from the analysis of algorithms for determining the maximum of a random walk, Random Structures and Algorithms, vol.10, issue.3, pp.333-335, 1997. ,
DOI : 10.1002/(SICI)1098-2418(199705)10:3<333::AID-RSA3>3.0.CO;2-X
Searching in an Unknown Environment: An Optimal Randomized Algorithm for the Cow-Path Problem, 4th ACM-SlAM Symp. Diserete Math, pp.441-447, 1993. ,
DOI : 10.1006/inco.1996.0092
The distribution of the maximum Brownian excursion, Journal of Applied Probability, vol.13, issue.02, pp.371-376, 1976. ,
DOI : 10.1007/BF00535106
On the random walk and Brownian motion, Transactions of the American Mathematical Society, vol.103, issue.2, pp.218-228, 1962. ,
DOI : 10.1090/S0002-9947-1962-0139211-2
Brownian local times and taboo processes, Transactions of the American Mathematical Society, vol.143, pp.173-185, 1969. ,
DOI : 10.1090/S0002-9947-1969-0253424-7
The art of computer programming: sorting and searching, 1997. ,
Tests concering random points on a circle, Indag. Math, vol.22, pp.38-47, 1960. ,
Une remarque sur les lois de certains temps d'atteinte, Sém. Pro. XV, Uni. Str, Lect. Notes Math, vol.80, issue.850, pp.669-670, 1979. ,
Kac's formula, levy's local time and brownian excursion, Journal of Applied Probability, vol.1, issue.03, pp.479-499, 1984. ,
DOI : 10.1214/aop/1176993927
Data Structures' Maxima, SIAM Journal on Computing, vol.26, issue.4, pp.1006-1042, 1997. ,
DOI : 10.1137/S0097539791196603
URL : https://hal.archives-ouvertes.fr/inria-00075166
An average case quasi-optimal algorithm for the search of zeros of a random walk, 1997. ,
Search for the maximum of a random walk, Random Structures and Aigorithms, pp.275-295, 1995. ,
Quelques identités en loi pour les processus de Bessel Hommage, Paris: Soc. Math. Fr., Astérisque, vol.236, pp.249-276, 1996. ,
Path decomposition of a Brownian bridge related to the ratio of its maximum and amplitude, Prépub, 1998. ,
Noisy information and computational complexity, 1996. ,
DOI : 10.1017/CBO9780511600814
A limit theorem for "Quicksort, RAIRO Inform. Thor. Appl, vol.25, issue.1, pp.85-100, 1991. ,
Continuous Martingales and Brownian Motion, 1994. ,
An introduction to the analysis of algorithms, 1996. ,
A formula of S, Ramanujan, J. Number Theory, vol.251, pp.1-19, 1987. ,
Honest bernoulli excursions, Journal of Applied Probability, vol.2, issue.03, pp.464-477, 1988. ,
DOI : 10.2307/3315033
Comparison methods for queues and other stochastic models, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, 1983. ,
The Wiener-Hopf equation whose kernel is a probability density, Duke math, J, vol.24, pp.327-343, 1957. ,
A Bernoulli excursion and its various applications, Adv. in Appl. Probab, vol.23, issue.3, pp.557-585, 1991. ,
Information-based complexity, 1988. ,
A relation between Brownian bridge and Brownian excursion, pp.143-149, 1979. ,
Path Decomposition and Continuity of Local Time for One-Dimensional Diffusions, I, Proc. London math. Soc., III. Ser, pp.738-768, 1974. ,
DOI : 10.1112/plms/s3-28.4.738
Diffusions, Markov processes, and martingales, Foundations. Wiley, vol.1, 1979. ,
Random Search in the Presence of Noise, with Application to Machine Learning, SIAM Journal on Scientific and Statistical Computing, vol.11, issue.4, pp.702-712, 1990. ,
DOI : 10.1137/0911041
Some aspects of Brownian motion. Part II. Some recent martingale problems, Lectures in Mathematics, 1997. ,
The continuum random tree. III Ann. of Probab, pp.248-289, 1993. ,
Brownian Excursion Conditioned on Its Local Time, Electronic Communications in Probability, vol.3, issue.0, pp.79-90, 1998. ,
DOI : 10.1214/ECP.v3-996
Valeurs principales associées aux temps locaux browniens, Bull. Sei. Maths, vol.111, pp.23-33, 1987. ,
The average height of planted plane trees, Graph Theory and Computing, pp.15-22, 1972. ,
How many questions are needed to find out the maximum of a Random Walk, press, Stoch. Proc. and Applns, 1999. ,
Introduction to Algorithm, 1990. ,
Parking functions, empirical processes and the width of rooted labe, 1999. ,
A Stochastically Quasi-Optimal Search Algorithm for the Maximum of the Simple Random Walk, 1999. ,
URL : https://hal.archives-ouvertes.fr/hal-00104835
A note on the stability of the local time of a wiener process, Stochastic Processes and their Applications, vol.25, pp.203-213, 1987. ,
DOI : 10.1016/0304-4149(87)90198-0
Some joint distributions for conditional random walks, Cano J. Stat, vol.14, pp.19-28, 1986. ,
Some remarks about the identity in law for the Bessel bridge rI ds, 1999. ,
On the profile of random trees, Random Structures and Algorithms, vol.10, issue.4, pp.421-466, 1997. ,
DOI : 10.1002/(SICI)1098-2418(199707)10:4<421::AID-RSA2>3.0.CO;2-W
Functionals of Brownian Meander and Brownian Excursion, The Annals of Probability, vol.5, issue.1, pp.130-135, 1977. ,
DOI : 10.1214/aop/1176995896
The average height of binary trees and other simple trees, Journal of Computer and System Sciences, vol.25, issue.2, 1982. ,
DOI : 10.1016/0022-0000(82)90004-6
URL : https://hal.archives-ouvertes.fr/inria-00076505
Introduction to the theory of random processes, 1969. ,
Semi-martingales et grossissement d'une jiltration, 17J Th. Jeulin Lecture Notes in Mathematics, vol.833, 1980. ,
The distribution of the maximum Brownian excursion, Journal of Applied Probability, vol.13, issue.02, pp.371-376, 1976. ,
DOI : 10.1007/BF00535106
The Art of Computer Programming, second edition, 1973. ,
Une approche élémentaire des théorèmes de décomposition de Williams, pp.447-464, 1986. ,
An average case quasi optimal algorithm for the search of ail the zeros of a random walk, p.44, 1997. ,
Search for the maximum of a random walk, Random Structures & Algorithms, vol.11, issue.2-3, pp.275-295, 1995. ,
DOI : 10.1007/978-94-011-3436-1
On the height of trees, Journal of the Australian Mathematical Society, vol.4, issue.04, pp.497-507, 1967. ,
DOI : 10.1007/BF02559539
Continuous martingales and Brownian motion, 1990. ,
Random walk in random and non-random environments, 1990. ,
An introduction to the analysis of algorithms, 1996. ,
A bernoulli excursion and its various applications, Advances in Applied Probability, vol.19, issue.03, pp.557-585, 1991. ,
DOI : 10.2307/2322249
On the distribution of the number of vertices in layers of random trees, Journal of Applied Mathematics and Stochastic Analysis, vol.4, issue.3, pp.175-186, 1991. ,
DOI : 10.1155/S104895339100014X
On the total heights of random rooted trees, Journal of Applied Probability, vol.174, issue.03, pp.543-556, 1992. ,
DOI : 10.1214/aop/1176993527
Random walk processes and their various applications, Pro. The. App., Essays to the Mem, of J. Mogyorodi, Math. Appl, vol.80, pp.1-32, 1992. ,
Limit distributions for queues and random rooted trees, Journal of Applied Mathematics and Stochastic Analysis, vol.6, issue.3, pp.189-216, 1993. ,
DOI : 10.1155/S1048953393000176
The continuum random tree. II: An overview. Stochastic analysis, Proc. Symp, pp.23-70, 1990. ,
The continuum random tree. III Ann. of Probab, pp.248-289, 1993. ,
Brownian excursions, critical random graphs and the multiplicative coalescent, The Annals of Probability, vol.25, issue.2, pp.812-854, 1997. ,
DOI : 10.1214/aop/1024404421
Deterministic and Stochastic Models for Coalescence (Aggregation and Coagulation): A Review of the Mean-Field Theory for Probabilists, Bernoulli, vol.5, issue.1, pp.3-48, 1999. ,
DOI : 10.2307/3318611
Random generation of trees, 1995. ,
DOI : 10.1007/978-1-4757-6353-9
A brief introduction to theta functions, 1961. ,
Valeurs principales associées aux temps locaux browniens, Bull. Sci. Maths Ill, pp.23-24, 1987. ,
DOI : 10.1007/bfb0084151
Pi and the AGM. A study in analytic number theory and computational complexity, 1998. ,
THE AVERAGE HEIGHT OF PLANTED PLANE TREES, pp.15-22, 1972. ,
DOI : 10.1016/B978-1-4832-3187-7.50007-6
A theorem on trees, Quarterly Journal of Pure and Applied Math, vol.23, pp.376-378, 1889. ,
DOI : 10.1017/CBO9780511703799.010
Phase transition for parking blocks, Brownian excursion and coalescence, 1999. ,
Excursions in Brownian motion, Arkiv f??r Matematik, vol.14, issue.1-2, pp.155-177, 1976. ,
DOI : 10.1007/BF02385832
A cluster of great formulas, Acta Mathematica Academiae Scientiarum Hungaricae, vol.48, issue.1-3, pp.65-67, 1982. ,
DOI : 10.1007/BF01895215
Strong approximations in probability and statistics. Probability and Mathematical Statistics, 1981. ,
On the profile of random trees, Random Structures and Algorithms, vol.10, issue.4, pp.421-451, 1997. ,
DOI : 10.1002/(SICI)1098-2418(199707)10:4<421::AID-RSA2>3.0.CO;2-W
Weak Convergence to Brownian Meander and Brownian Excursion, The Annals of Probability, vol.5, issue.1, pp.117-129, 1977. ,
DOI : 10.1214/aop/1176995895
URL : http://doi.org/10.1214/aop/1176995895
The average height of binary trees and other simple trees, Journal of Computer and System Sciences, vol.25, issue.2, 1982. ,
DOI : 10.1016/0022-0000(82)90004-6
URL : https://hal.archives-ouvertes.fr/inria-00076505
On the Analysis of Linear Probing Hashing, Algorithmica, vol.22, issue.4, pp.490-515, 1998. ,
DOI : 10.1007/PL00009236
URL : https://hal.archives-ouvertes.fr/inria-00073424
Mappings of acyclic and parking functions. Aequationes math, VoL, vol.10, pp.10-22, 1974. ,
Acyclic and parking functions, Journal of Combinatorial Theory, Series A, vol.18, issue.1, pp.27-35, 1975. ,
DOI : 10.1016/0097-3165(75)90063-1
Independent and stationary sequences of random variables, 1971. ,
Semi-martingales et grossissement d'une filtration, Lecture Notes in Mathematics, vol.833, 1980. ,
An Invariance Principle for Random Walk Conditioned by a Late Return to Zero, The Annals of Probability, vol.4, issue.1, pp.115-121, 1976. ,
DOI : 10.1214/aop/1176996189
Some problems in the theory of queues, J. of the Roy, Stat. Soc. B, vol.13, pp.151-185, 1951. ,
On the average stack size of regularly distributed binary trees, Lect. Notes in Comp. Sei. 71, pp.340-355, 1979. ,
DOI : 10.1007/3-540-09510-1_28
The distribution of the maximum Brownian excursion, Journal of Applied Probability, vol.13, issue.02, pp.371-376, 1976. ,
DOI : 10.1007/BF00535106
The art of computer programming, 1997. ,
The art of computer programming: sorting and searching, 1997. ,
Linear Probing and Graphs, Algorithmica, vol.22, issue.4, pp.561-568, 1998. ,
DOI : 10.1007/PL00009240
An Occupancy Discipline and Applications, SIAM Journal on Applied Mathematics, vol.14, issue.6, pp.1266-1274, 1966. ,
DOI : 10.1137/0114101
Kac's formula, levy's local time and brownian excursion, Journal of Applied Probability, vol.1, issue.03, pp.479-499, 1984. ,
DOI : 10.1214/aop/1176993927
Counting labelled trees, Canadian Mathematical Monographs, issue.1, 1970. ,
Combinatorial algorithms, 1975. ,
Bandwidths and profiles of trees, Journal of Combinatorial Theory, Series B, vol.42, issue.3, pp.348-370, 1987. ,
DOI : 10.1016/0095-8956(87)90052-9
The Multiplicative Process, The Annals of Mathematical Statistics, vol.20, issue.2, pp.206-224, 1949. ,
DOI : 10.1214/aoms/1177730031
URL : http://doi.org/10.1214/aoms/1177730031
Sums of independant random variables, 1975. ,
Enumerations of trees and forests related ta bran ching processes and random walks, Microsurveys in Discrete Probability, 1998. ,
A polytope related ta empirical distributions, plane trees, parking functions, and the associahedron Linear probing: the probable largest search time grows logarithmically with the number of records, J. AIgorithms, vol.8, issue.2, pp.236-249, 1987. ,
Convergence of stochastic processes. Springer Series in Statistics, 1984. ,
On the height of trees, Journal of the Australian Mathematical Society, vol.4, issue.04, pp.497-507, 1967. ,
DOI : 10.1007/BF02559539
On an enumeration problem, Journal of Combinatorial Theory, vol.4, issue.3, pp.219-241, 1968. ,
DOI : 10.1016/S0021-9800(68)80003-1
An introduction ta the analysis of algorithms, 1996. ,
Empirical processes with applications ta statistics, 1986. ,
Honest bernoulli excursions, Journal of Applied Probability, vol.2, issue.03, pp.464-477, 1988. ,
DOI : 10.2307/3315033
Enumerating graphs and Brownian motion, Communications on Pure and Applied Mathematics, vol.50, issue.3, pp.291-294, 1997. ,
DOI : 10.1002/(SICI)1097-0312(199703)50:3<291::AID-CPA4>3.0.CO;2-6
The complexity of drawing trees ni cely. Acta Inform, pp.377-392, 1982. ,
On the total heights of random rooted trees, J. Appl. Probab, vol.29, issue.3, pp.543-556, 1992. ,
Limit distributions for queues and random rooted trees, Journal of Applied Mathematics and Stochastic Analysis, vol.6, issue.3, pp.189-216, 1993. ,
DOI : 10.1155/S1048953393000176
Searching in the plane, Inf. Comput, vol.106, issue.2, pp.234-252, 1993. ,
Dynamic programming, 1947. ,
An introduction to probability theory and its applications, 1966. ,
Reasoning under varying and uncertain constraints, Seventh National Conference on Artificial Intelligence, pp.11-116, 1988. ,
Optimizing decision quality with contract algorithms, 14 th international joint conference on artificial intelligence 49, pp.1576-1582, 1995. ,
Real-Time Problem-Solving with Contract Algorithm, th international joint conference on artificial intelligence, 1999. ,
Optimal composition of real-time systems, Artificial Intelligence, vol.82, issue.1-2, pp.181-213, 1996. ,
DOI : 10.1016/0004-3702(94)00074-3
4, 15, 13. Il est clair que la forme de l'arbre ne dépend pas de la valeur des étiquettes, mais seulement de l'ordre des Xi' Supposons que les nombres Xi soient des v.a. uniformes indépendantes sur [0, 1]. Il est facile de voir que la permutation 0-de Sn (le groupe symétrique), telle que XO < xO"(n) suit également la loi uniforme sur Sn. L'ensemble des arbres binaires de recherche est classiquement muni de la loi induite par l'équiprobabilité sur Sn, noeuds internes sont les noeuds de T n . Par exemple Muni de cette loi, les ABR ne sont pas des arbres de G.W.. ? Pour s'en convaincre ,
fils" est inférieure à toutes les autres et il yan -1 façons de construire cet arbre; il suffit que tous les autres étiquettes soient rangées par ordre croissant ,
Par exemple, la hauteur d'un ABR est de l'ordre de logn contre ,;n pour les arbres de G.W .. On pourra se référer aux livres de Knuth, Sedegewick et Flajolet [43] ainsi qu'aux articles de L. Devroye ,
on définit les familles d'arbres simples non pas par une loi de reproduction mais par une équation fonctionnelle ,
issue de Aldous [1], permet de passer d'une définition combinatoire des arbres à une définition probabiliste et réciproquement ,
The continuum random tree. III, Ann. Probab, pp.248-289, 1993. ,
Brownian excursions, critical random graphs and the multiplicative coalescent, The Annals of Probability, vol.25, issue.2, pp.812-854, 1997. ,
DOI : 10.1214/aop/1024404421
Branching processes, Progress in Prob. and Stat., Birkhaeuser, 1983. ,
Path transformations connecting Brownian bridge, excursion and meander, Bull. Sei. Math., II. Ser, vol.118, issue.2, pp.147-166, 1994. ,
Relations entre pont et excursion du mouvement brownien reel, Probab. Stat, vol.22, pp.1-7, 1986. ,
Convergence of probability measures, 1968. ,
DOI : 10.1002/9780470316962
Probability and measure, Wiley Series in Prob. and math, 1979. ,
Handbook of Brownian Motion -Facts and Formulae, 1996. ,
Valeurs principales associées aux temps locaux browniens, Bull. Sei. Maths, vol.111, pp.23-24, 1987. ,
DOI : 10.1007/bfb0084151
Excursions in Brownian motion, Arkiv f??r Matematik, vol.14, issue.1-2, pp.155-177, 1976. ,
DOI : 10.1007/BF02385832
Introduction to Algorithm, 1990. ,
Some joint distributions for conditional random walks, Canadian Journal of Statistics, vol.26, issue.1, pp.19-28, 1986. ,
DOI : 10.2307/3315033
On the profile of random trees, Random Struet, Algorithms, vol.10, issue.4, pp.421-451, 1997. ,
Branching processes in the analysis of the heights of trees, Acta Informatica, vol.24, issue.3, pp.277-298, 1987. ,
DOI : 10.1007/BF00265991
Functionals of Brownian Meander and Brownian Excursion, The Annals of Probability, vol.5, issue.1, pp.130-135, 1977. ,
DOI : 10.1214/aop/1176995896
A Fluctuation Theorem for Cyclic Random Variables, The Annals of Mathematical Statistics, vol.33, issue.4, pp.1450-1453, 1962. ,
DOI : 10.1214/aoms/1177704376
The total progeny in a branching process and a related random walk, Journal of Applied Probability, vol.1, issue.03, pp.682-686, 1969. ,
DOI : 10.1007/BF00531752
The average height of binary trees and other simple trees, Journal of Computer and System Sciences, vol.25, issue.2, pp.171-213, 1982. ,
DOI : 10.1016/0022-0000(82)90004-6
URL : https://hal.archives-ouvertes.fr/inria-00076505
Mappings of acyclic and parking functions, Aequationes Mathematicae, vol.4, issue.1, pp.10-22, 1974. ,
DOI : 10.1007/BF01834776
Acyclic and parking functions, Journal of Combinatorial Theory, Series A, vol.18, issue.1, pp.27-35, 1975. ,
DOI : 10.1016/0097-3165(75)90063-1
Semi-martingales et grossissement d'une filtration, Lecture Notes in Mathematics, vol.833, 1980. ,
The theory of branching processes, 1963. ,
DOI : 10.1007/978-3-642-51866-9
Brownian motion and stochastic calculus, 1988. ,
On the stack size of regularly distributed binary trees, Proceedings, 6th ICALP Conf, 1979. ,
The Galton-Watson process conditioned on the total progeny, Journal of Applied Probability, vol.13, issue.04, pp.800-806, 1975. ,
DOI : 10.1017/S0001867800037629
The art of computer programming, 1968. ,
Une approche élémentaire des théorèmes de décomposition de Williams, Sém. Prob. XX, pp.447-464, 1986. ,
Branching processes in Lévy processes : The exploration process, 1996. ,
Kac's formula, levy's local time and brownian excursion, Journal of Applied Probability, vol.1, issue.03, pp.479-499, 1984. ,
DOI : 10.1214/aop/1176993927
The brownian excursion area: a numerical analysis, Computers & Mathematics with Applications, vol.10, issue.6, pp.413-417, 1984. ,
DOI : 10.1016/0898-1221(84)90071-3
Erratum: The Brownian excursion area : a numerical analysis, Comput. Math. Appl, p.375, 1986. ,
Counting labelled trees, Canadian Mathematical Monographs, issue.1, 1970. ,
The Multiplicative Process, The Annals of Mathematical Statistics, vol.20, issue.2, pp.206-224, 1949. ,
DOI : 10.1214/aoms/1177730031
Convergence of stochastic processes, 1984. ,
DOI : 10.1007/978-1-4612-5254-2
On the height of trees, Journal of the Australian Mathematical Society, vol.4, issue.04, pp.497-507, 1967. ,
DOI : 10.1007/BF02559539
Random walk in random and non-random environments, 1990. ,
Continuous martingales and Brownian motion, pp.9-10, 1990. ,
The Enumeration of Trees by Height and Diameter, IBM Journal of Research and Development, vol.4, issue.5, pp.473-478, 1960. ,
DOI : 10.1147/rd.45.0473
An introduction to the analysis of algorithms, 1996. ,
On an enumeration problem, Journal of Combinatorial Theory, vol.4, issue.3, pp.219-241, 1968. ,
DOI : 10.1016/S0021-9800(68)80003-1
Enumerating graphs and Brownian motion, Communications on Pure and Applied Mathematics, vol.50, issue.3, pp.291-294, 1997. ,
DOI : 10.1002/(SICI)1097-0312(199703)50:3<291::AID-CPA4>3.0.CO;2-6
Principes of Random Walk, p.6, 1964. ,
A Bernoulli excursion and its various applications, Adv. App!. Prob, vol.23, pp.557-585, 1991. ,
Random walk processes and their various applications, Probability theory and applications, Essays to the Mem, of J. Mogyorodi, Math. App!, vol.80, pp.1-32, 1992. ,
Limit distributions for queues and random rooted trees, Journal of Applied Mathematics and Stochastic Analysis, vol.6, issue.3, pp.189-216, 1993. ,
DOI : 10.1155/S1048953393000176
Brownian local times, Journal of Applied Mathematics and Stochastic Analysis, vol.8, issue.3, pp.209-232, 1995. ,
DOI : 10.1155/S1048953395000207
A Relation between Brownian Bridge and Brownian Excursion, The Annals of Probability, vol.7, issue.1, pp.143-149, 1979. ,
DOI : 10.1214/aop/1176995155
URL : http://doi.org/10.1214/aop/1176995155