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The existence and uniqueness of the solution of an integral equation driven by a $p$-semimartingale of special type. (English) Zbl 1059.60068
Existence and uniqueness of adapted solution with almost all sample paths in the space of continuous functions with a bounded $q$-variation is proved for the equation $$X_t = \xi + \int _0^t f(X_s)\,dW_s + \int _0^t g(X_s)\,dB^H_s,\quad 0\le t\le T,$$ where $W$ and $B^H$ denote the standard Brownian motion and the fractional Brownian motion with the Hurst parameter $H\in (1/2,1)$, respectively, $f$ is a Lipschitz function on $\Bbb R$ and $g\in C^{1+\alpha }(\Bbb R)$, if $0<\alpha <1,\ 1/H<p<2$ are such that $\alpha /q + 1/p >1$.

60H05Stochastic integrals
60H10Stochastic ordinary differential equations
Full Text: DOI
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