The existence and uniqueness of the solution of an integral equation driven by a p-semimartingale of special type

K. Kubilius

Stochastic Processes and their Applications, 2002, vol. 98, issue 2, 289-315

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.

Keywords: Stochastic; integral; equation; Fractional; Brownian; motion; p-variation; p-semimartingales (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (8)

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