Linear backward stochastic differential equations with Gaussian Volterra processes Article - Décembre 2020

H Knani, M Dozzi

H Knani, M Dozzi, « Linear backward stochastic differential equations with Gaussian Volterra processes  », Modern Stochastics : Theory and Applications, décembre 2020, pp. 415-433. ISSN 2351-6046

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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