| Title:
|
Weak averaging of stochastic evolution equations (English) |
| Author:
|
Vrkoč, Ivo |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
120 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
91-111 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A theorem on continuous dependence of solutions to stochastic evolution equations on coefficients is established, covering the classical averaging procedure for stochastic parabolic equations with rapidly oscillating both the drift and the diffusion term. (English) |
| Keyword:
|
stochastic evolution equations |
| Keyword:
|
averaging methods |
| Keyword:
|
weak convergence |
| MSC:
|
60H10 |
| MSC:
|
60H15 |
| idZBL:
|
Zbl 0849.60067 |
| idMR:
|
MR1336949 |
| DOI:
|
10.21136/MB.1995.125891 |
| . |
| Date available:
|
2009-09-24T21:09:24Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125891 |
| . |
| Reference:
|
[1] S. Chevet: Compacité dans l'espace des probabilités de Radon gaussiennes sur un Banach.C. R. Acad. Sci. Paris Ser. I Math. 296 (1983), 275-278. Zbl 0538.60006, MR 0693792 |
| Reference:
|
[2] G. Da Prato J. Zabczyk: Stochastic equations in infinite dimensions.Cambridge University Press, Cambridge, 1992. MR 1207136 |
| Reference:
|
[3] R. M. Dudley: Real analysis and probability.Wadsworth & Brook/Cole, Pacific Grove, 1989. Zbl 0686.60001, MR 0982264 |
| Reference:
|
[4] И. И. Гuxмaн: Диффepeнциaльныe ypaвнeния co cлyчaйными фyнкциями.Зимняя шкoлa пo тeopии вepoятнocтeй и мaтeмaтичecкoй cтaтиcтикe (Ужгopoд, 1964). Инcт. Maт. Укpaин. CCP, Kиeв, 1964, cтp. 41-85. |
| Reference:
|
[5] P. 3. Xacьмuнcкuй: O пpинципe ycpeднeния для пapaбoличecкиx и эллиптичecкиx диффepeнциaльныx ypaвнeний и мapкoвcкиx пpoцeccoв c мaлoй диффyзиeй.Teop. Bepoятнocт. и Пpимeнeн. 8 (1963), 3-25. |
| Reference:
|
[6] P. 3. Xacьмuнcкuй: O пpинципe ycpeднeния для cтoxacтичecкиx диффepeнциaльныx ypaвнeний Итo.Kybernetika Ą (1968), 260-279. |
| Reference:
|
[7] B. Maslowski J. Seidler I. Vrkoč: An averaging principle for stochastic evolution equations II.Math. Bohem. 116 (1991), 191-224. MR 1112004 |
| Reference:
|
[8] B. Maslowski J. Seidler I. Vrkoč: Integral continuity and stability for stochastic hyperbolic equations.Differential Integral Equations 6 (1993), 355-382. MR 1195388 |
| Reference:
|
[9] J. Seidler: Da Prato-Zabczyk's maximal inequality revisited I.Math. Bohem. 118 (1993), 67-106. Zbl 0785.35115, MR 1213834 |
| Reference:
|
[10] J. Seidler I. Vrkoč: An averaging principle for stochastic evolution equations.Čas. Pěst. Mat. 115 (1990), 240-263. MR 1071056 |
| Reference:
|
[11] A. B. Cкopoxoд: Acимптoтичecкиe мeтoды тeopии cтoxacтичecкиx диффepeнциaльныx ypaвнeний.Hayкoвa Дyмкa, Kиeв, 1987. |
| Reference:
|
[12] I. Vrkoč: Extension of the averaging method to stochastic equations.Czechoslovak Math. J. 16 (91) (1966), 518-544. MR 0205318 |
| . |
