Speaker: G/Shevchenko
Title: Stochastic differential equations with mixed noise (based on Doctor’s thesis)
The talk will be devoted to so-called “mixed” stochastic differential equations
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0 ∫ a(s,X(s))ds+ t |
0 ∫ b(s,X(s))dW(s)+ t |
0 ∫ c(s,X(s))dZ(s), t |
where W is a standard Wiener process, Z is an adapted process trajectories of which almost surely satisfy the Holder condition with constant γ>1/2. Results on existence, uniqueness and integrability of the solution of this equation will be discussed. In case when Z=BH is a fractal Brownian motion with Hurst parameter >1/2 also conditions of Malliavin differentiability and existence of the solution’s density will be given.