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Malliavin regularity of solutions to mixed stochastic differential equations

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  • Shevchenko, Georgiy
  • Shalaiko, Taras

Abstract

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

Suggested Citation

  • Shevchenko, Georgiy & Shalaiko, Taras, 2013. "Malliavin regularity of solutions to mixed stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2638-2646.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:12:p:2638-2646
    DOI: 10.1016/j.spl.2013.08.013
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    References listed on IDEAS

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    1. Nualart, David & Saussereau, Bruno, 2009. "Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 391-409, February.
    2. Kubilius, K., 2002. "The existence and uniqueness of the solution of an integral equation driven by a p-semimartingale of special type," Stochastic Processes and their Applications, Elsevier, vol. 98(2), pages 289-315, April.
    3. Nourdin, Ivan & Simon, Thomas, 2006. "On the absolute continuity of one-dimensional SDEs driven by a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 907-912, May.
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    1. Mishura, Yuliya & Shalaiko, Taras & Shevchenko, Georgiy, 2015. "Convergence of solutions of mixed stochastic delay differential equations with applications," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 487-497.

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