GENERALIZED STOCHASTIC PERTURBATION-DEPENDING DIFFERENTIAL EQUATIONS

The paper is devoted to the generalized stochastic differential equations of the Itoˆ type whose coefficients are additionally perturbed and dependent on a small parameter. Their solutions are compared with the solutions of the corresponding unperturbed equations. We give conditions under which the...

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Bibliographic Details
Published inStochastic analysis and applications Vol. 20; no. 6; pp. 1281 - 1307
Main Authors JANKOVIC, Svetlana, JOVANOVIC, Miljana
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Taylor & Francis Group 31.12.2002
Taylor & Francis
Subjects
AMS Mathematics Subject Classification : 60H10
Closeness in the (2m)-th mean
Exact sciences and technology
Generalized stochastic differential equation
Mathematics
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Small perturbations
Stochastic analysis
Itô equation
Probabilistic approach
Gaussian noise
Differential equation
Generalized equation
White noise
Parameter variation
Small perturbation
Stochastic equation
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Summary:The paper is devoted to the generalized stochastic differential equations of the Itoˆ type whose coefficients are additionally perturbed and dependent on a small parameter. Their solutions are compared with the solutions of the corresponding unperturbed equations. We give conditions under which the solutions of these equations are close in the (2m)-th moment sense on finite intervals or on intervals whose length tends to infinity as the small parameter tends to zero. We also give the degree of the closeness of these solutions.
ISSN:0736-2994
1532-9356
DOI:10.1081/SAP-120015833