The existence and uniqueness of the solution of an integral equation driven by a p-semimartingale of special type |
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Institution: | Institute of Mathematics and Informatics, Akademijos 4, Vilnius 2600, Lithuania |
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Abstract: | We consider the integral equation driven by a standard Brownian motion and fractional Brownian motion (fBm). Since fBm is not a semimartingale, we cannot use the semimartingale theory to define an integral with respect to the fBm. Furthermore, a well-developed theory of stochastic differential equations is not applicable to solve it. Existence and uniqueness conditions are obtained for a solution in the space of continuous functions with q-bounded variation, q>2. |
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