Malliavin regularity of solutions to mixed stochastic differential equations

DOI10.1016/j.spl.2013.08.013zbMath1287.60075arXiv1305.3462OpenAlexW1990078817MaRDI QIDQ2439634

Taras Shalaiko, Georgiy M. Shevchenko

Publication date: 14 March 2014

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.3462

zbMATH Keywords

Wiener processfractional Brownian motionmixed stochastic differential equationMalliavin regularity

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (10)

Exponential stability for neutral stochastic functional partial differential equations driven by Brownian motion and fractional Brownian motion ⋮ Existence of Density for Solutions of Mixed Stochastic Equations ⋮ Rate of convergence of Euler approximation of time-dependent mixed SDEs driven by Brownian motions and fractional Brownian motions ⋮ Convergence of solutions of mixed stochastic delay differential equations with applications ⋮ Mixed stochastic delay differential equations ⋮ Integrability of solutions to mixed stochastic differential equations ⋮ The existence, uniqueness, and controllability of neutral stochastic delay partial differential equations driven by standard Brownian motion and fractional Brownian motion ⋮ Existence and uniqueness for solutions of mixed stochastic delay differential equations ⋮ Existence and exponential stability in the \(p\)th moment for impulsive neutral stochastic integro-differential equations driven by mixed fractional Brownian motion ⋮ Stability of a class of impulsive neutral stochastic functional partial differential equations

Cites Work

• Mixed stochastic differential equations with long-range dependence: existence, uniqueness and convergence of solutions
• Smoothness of the density for solutions to Gaussian rough differential equations
• Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion
• Differential equations driven by fractional Brownian motion
• Mixed fractional Brownian motion
• The existence and uniqueness of the solution of an integral equation driven by a \(p\)-semimartin\-gale of special type.
• On the absolute continuity of one-dimensional SDEs driven by a fractional Brownian motion
• A version of Hörmander's theorem for the fractional Brownian motion
• Existence and Uniqueness of the Solution of Stochastic Differential Equation Involving Wiener Process and Fractional Brownian Motion with Hurst IndexH > 1/2
• The Malliavin Calculus and Related Topics
• Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion
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