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Journal Articles Modern Stochastics: Theory and Applications Year : 2020

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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Dates and versions

hal-02384407 , version 1 (28-11-2019)
hal-02384407 , version 2 (20-07-2021)

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