Malliavin regularity of solutions to mixed stochastic differential equations

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.

References in corpus (5)

• Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion
• Smoothness of the density for solutions to Gaussian rough differential equations
• Mixed stochastic differential equations with long-range dependence: existence, uniqueness and convergence of solutions
• Stochastic differential equation involving Wiener process and fractional Brownian motion with Hurst index $H>1/2$
• Mixed fractional stochastic differential equations with jumps

Cited by in corpus (2)

• Convergence of solutions of mixed stochastic delay differential equations with applications
• Integrability of solutions to mixed stochastic differential equations