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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| Published in | Stochastic analysis and applications Vol. 20; no. 6; pp. 1281 - 1307 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia, PA
Taylor & Francis Group
31.12.2002
Taylor & Francis |
| Subjects | |
| Online Access | Get full text |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Jankovic´, Svetlana Jovanovic´, Miljana |
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| Cites_doi | 10.1007/978-1-4757-1665-8 10.1155/S104895339600024X 10.1007/978-94-015-8034-2 10.2996/kmj/1138037145 |
| ContentType | Journal Article |
| Copyright | Copyright Taylor & Francis Group, LLC 2002 2003 INIST-CNRS |
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| EndPage | 1307 |
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| Issue | 6 |
| Keywords | Itô equation Probabilistic approach Gaussian noise Differential equation Generalized equation White noise Parameter variation Small perturbation Stochastic equation |
| Language | English |
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| References | Berger M.A. (cit5833-5) 1980; 2 Liptser R. (cit5833-6) 1977 Itô K. (cit5833-1) 1951; 4 cit5833-3 Murge M.G. (cit5833-2) 1986; 34 cit5833-7 Murge M.G. (cit5833-4) 1990; 21 Bainov D. (cit5833-10) 1992 Janković S.V. (cit5833-8) 2000; 30 Ladde G. (cit5833-11) 1980 |
| References_xml | – volume-title: Statistics of Random Processes I year: 1977 ident: cit5833-6 doi: 10.1007/978-1-4757-1665-8 – volume-title: Random Differential Inequalities year: 1980 ident: cit5833-11 – volume: 4 start-page: 1 year: 1951 ident: cit5833-1 publication-title: Meml Math. Soc. – volume: 30 start-page: 133 year: 2000 ident: cit5833-8 publication-title: Novi Sad J. Math., Novi Sad – volume: 21 start-page: 260 year: 1990 ident: cit5833-4 publication-title: Indian J. Pure Appl. Math. – volume: 2 start-page: 187 year: 1980 ident: cit5833-5 publication-title: J. Integral Equations – volume: 34 start-page: 23 year: 1986 ident: cit5833-2 publication-title: Yokohama Math. J. – ident: cit5833-7 doi: 10.1155/S104895339600024X – volume-title: Integral Inequalities and Applications year: 1992 ident: cit5833-10 doi: 10.1007/978-94-015-8034-2 – ident: cit5833-3 doi: 10.2996/kmj/1138037145 |
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| SubjectTerms | 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 |
| Title | GENERALIZED STOCHASTIC PERTURBATION-DEPENDING DIFFERENTIAL EQUATIONS |
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