Integrability of solutions to mixed stochastic differential equations

Abstract

We prove that the standard conditions that provide unique solvability of a mixed stochastic differential equations also guarantee that its solution possesses finite moments. We also present conditions supplying existence of exponential moments. For a special equation whose coefficients do not satisfy the linear growth condition, we find conditions for integrability of its solution.

References in corpus (4)

• Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion
• 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 $H>1/2$
• Malliavin regularity of solutions to mixed stochastic differential equations