The existence and uniqueness of the solution of an integral equation driven by a \(p\)-semimartin\-gale of special type.
type: Item
instance of: scholarly article
title: The existence and uniqueness of the solution of an integral equation driven by a \(p\)-semimartin\-gale of special type.
zbMATH Open document ID: 1059.60068
DOI: 10.1016/S0304-4149(01)00145-4
published in: Stochastic Processes and their Applications
publication date: 2005-02-25T00:00:00Z
review text: 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 \(\alpha /q + 1/p >1\).
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 2138957
zbMATH Keywords: stochastic equation
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: \(p\)-martingales
author: K. Kubilius
MaRDI profile type: Publication
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Wikidata QID: Q127065577
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description: scientific article; zbMATH DE number 2138957