## 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 $X_t = \xi + \int _0^t f(X_s)\,dW_s + \int _0^t g(X_s)\,dB^H_s,\quad 0\leq t\leq T,$ 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 $$\mathbb R$$ and $$g\in C^{1+\alpha }(\mathbb R)$$, if $$0<\alpha <1,\;1/H<p<2$$ are such that $$\alpha /q + 1/p >1$$.

### MSC:

 60H05 Stochastic integrals 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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### References:

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