Malliavin regularity of solutions to mixed stochastic differential equations

TL;DR

This paper investigates the Malliavin regularity of solutions to mixed stochastic differential equations driven by fractional Brownian motions and Wiener processes, establishing their derivatives' existence, integrability, and exponential moments.

Contribution

It provides new results on the Malliavin differentiability and exponential integrability of solutions to mixed stochastic differential equations involving fractional Brownian motion.

Findings

Existence of Malliavin derivatives for the solutions.

Integrability of the Malliavin derivatives.

Solutions possess exponential moments.

Abstract

For a mixed stochastic differential driven by independent fractional Brownian motions and Wiener processes, the existence and integrability of the Malliavin derivative of its solution are established. It is also proved that the solution possesses exponential moments.