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Matematicheskie Zametki, 2009, Volume 86, Issue 4, Pages 525–537
DOI: https://doi.org/10.4213/mzm4135 (Mi mzm4135) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Two-Parameter Stochastic Volterra Equations

N. A. Kolodij

Volgograd State University
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DOI: https://doi.org/10.4213/mzm4135
Abstract: We study two-parameter stochastic Volterra equations containing integrals over strong martingales and fields of bounded variation. For such equations, we prove the existence and uniqueness theorems for solutions with trajectories in the space of Borel functions which are locally square-integrable with respect to a locally finite measure. Under additional conditions on the coefficients of the equation, we prove the existence of a modification of the solution with trajectories continuous on the right and without discontinuities of the second kind.
Keywords: stochastic Volterra equation, martingale, Borel function, metric separable space, stochastic integral, Hölder's inequality.
Received: 04.07.2007
Revised: 02.02.2009
English version:
Mathematical Notes, 2009, Volume 86, Issue 4, Pages 493–504
DOI: https://doi.org/10.1134/S0001434609090259
Bibliographic databases:
UDC: 519.21
Language: Russian
Citation: N. A. Kolodij, “Two-Parameter Stochastic Volterra Equations”, Mat. Zametki, 86:4 (2009), 525–537; Math. Notes, 86:4 (2009), 493–504
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    1. Guo JIANG, Xiangjun WANG, “Regularity property of solution to two-parameter stochastic volterra equation with non-lipschitz coefficients”, Acta Mathematica Scientia, 33:3 (2013), 872  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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