On Volterra type stochastic integrals with respect to a continuous strong martingale (Q2777842)
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scientific article; zbMATH DE number 1718885
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Volterra type stochastic integrals with respect to a continuous strong martingale |
scientific article; zbMATH DE number 1718885 |
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13 March 2002
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strong martingale
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stochastic integral
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continuous modification
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inequality for moments
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On Volterra type stochastic integrals with respect to a continuous strong martingale (English)
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The author deals with stochastic integrals with respect to two-parameter continuous strong square-integrable martingales whose integrands depend on limits of integration. Existence of a continuous modification of the Volterra type stochastic integral is proved under conditions which contain weaker regularity condition than the Hölder condition. An inequality for moments of continuous modifications of such integrals is proposed. For more details see, for example, \textit{A. M. Kolodij} [Theory Stoch. Process. 4(20), No. 1-2, 133-138 (1998; Zbl 0939.60072)] and \textit{Yu. S. Mishura} [Theory Probab. Math. Stat. 49, 123-136 (1994); translation from Teor. Jmovirn. Mat. Stat. 49, 173-192 (1993; Zbl 0861.60067)].
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