Time reversal of Volterra processes driven stochastic differential equation

TL;DR

This paper investigates how stochastic differential equations driven by Volterra processes behave under time reversal, transforming into past-dependent equations driven by Brownian motion, and establishes conditions for their solutions' existence and uniqueness.

Contribution

It introduces a novel approach to analyze Volterra-driven SDEs through time reversal, enabling the derivation of existence and uniqueness results.

Findings

Time reversal transforms Volterra-driven SDEs into past-dependent equations.

Existence and uniqueness of solutions are established under this transformation.

Provides a new framework for analyzing complex stochastic systems.

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.