Existence of density for solutions of mixed stochastic equations

Taras Shalaiko; Georgiy Shevchenko

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arXiv · 1406.1896

Existence of density for solutions of mixed stochastic equations

Taras Shalaiko·Georgiy Shevchenko

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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.

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Taras Shalaiko, Georgiy Shevchenko. 2014-06-07. Existence of density for solutions of mixed stochastic equations. https://arxiv.org/abs/1406.1896

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