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Linear backward stochastic differential equations with Gaussian Volterra processes

Abstract : Explicit solutions for a class of linear backward stochastic differential equations (BSDE) driven by Gaussian Volterra processes are given. These processes include the multifractional Brownian motion and the multifractional Ornstein-Uhlenbeck process. By an Itô formula, proven in the context of Malliavin calculus, the BSDE is associated to a linear second order partial differential equation with terminal condition whose solution is given by a Feynman-Kac type formula.
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https://hal.univ-lorraine.fr/hal-02384407
Contributor : Habiba Knani Connect in order to contact the contributor
Submitted on : Tuesday, July 20, 2021 - 3:26:42 PM
Last modification on : Wednesday, November 3, 2021 - 7:10:33 AM

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H Knani, M Dozzi. Linear backward stochastic differential equations with Gaussian Volterra processes. Modern Stochastics: Theory and Applications, VTEX, 2020, 7 (4), pp.415-433. ⟨10.15559/20-VMSTA166⟩. ⟨hal-02384407v2⟩

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