Existence of density for solutions of mixed stochastic equations

Taras Shalaiko; Georgiy Shevchenko

Existence of density for solutions of mixed stochastic equations

Probability 2014-06-10 v1

Authors: Taras Shalaiko , Georgiy Shevchenko

Abstract

We consider a mixed stochastic differential equation $d{X_t}=a(t,X_t)d{t}+b(t,X_t) d{W_t}+c(t,X_t)d{B^H_t}$ driven by independent multidimensional Wiener process and fractional Brownian motion. Under Hormander type conditions we show that the distribution of $X_t$ possesses a density with respect to the Lebesgue measure.

Keywords

mixed stochastic differential equations fractional Brownian motion Wiener process density of distribution H\"ormander conditions Lebesgue measure

Cite

@article{arxiv.1406.1896,
  title  = {Existence of density for solutions of mixed stochastic equations},
  author = {Taras Shalaiko and Georgiy Shevchenko},
  journal= {arXiv preprint arXiv:1406.1896},
  year   = {2014}
}

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