Time reversal of Volterra processes driven stochastic differential equation

2010/08/17 by Laurent Decreusefond, Decreusefond, Laurent
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Numerical methods in inverse problems #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1008.2850

openalex publication_date 2010/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider stochastic differential equations driven by some Volterra processes. Under time reversal, these equations are transformed into past dependent stochastic differential equations driven by a standard Brownian motion. We are then in position to derive existence and uniqueness of solutions of the Volterra driven SDE considered at the beginning.

Citations

• A Lévy area by Fourier normal ordering for multidimensional fractional Brownian motion with small Hurst index

Related

• Partial differential equations associated to non linear backward stochastic differential equations with Gaussian Volterra processes
• The unique solution of stochastic differential equations
• Linear Volterra backward stochastic differential equations
• Reflected backward doubly stochastic differential equations with time delayed generators
• Linear Backward Stochastic Differential Equations with Gaussian Volterra processes