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Etude de processus stochastiques non linéaires

Abstract : Our study deals with processes which are solutions of stochastic differential equations in which the law of the solution can interact . We etablish an instability phenomena for a two-dimensional stochastic process which density verifies a P.D.E. of Burgers' type: the solution fluctuates when the diffusion tends to zero. For an ordinary S.D.E with inward drift, we study the asymptotic behaviour of hitting times for the process to a fixed point when the starting point goes to infinity . We consider another equation with inward drift which is more non linear and reflected in a real interval and we prove that the process tends in law to a unique stationnary measure . We solve a simulation problem for a two-dimensional stochastic process composed of a one-dimensional process and an integral related to this process .
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https://hal.univ-lorraine.fr/tel-01747520
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Sophie Wantz Mézières. Etude de processus stochastiques non linéaires. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 1997. Français. ⟨NNT : 1997NAN10163⟩. ⟨tel-01747520⟩

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