Weak averaging of stochastic evolution equations

Ivo Vrkoč

Mathematica Bohemica (1995)

  • Volume: 120, Issue: 1, page 91-111
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Vrkoč, Ivo. "Weak averaging of stochastic evolution equations." Mathematica Bohemica 120.1 (1995): 91-111. <http://eudml.org/doc/247786>.

@article{Vrkoč1995,
abstract = {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.},
author = {Vrkoč, Ivo},
journal = {Mathematica Bohemica},
keywords = {stochastic evolution equations; averaging methods; weak convergence; stochastic evolution equations; averaging methods},
language = {eng},
number = {1},
pages = {91-111},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weak averaging of stochastic evolution equations},
url = {http://eudml.org/doc/247786},
volume = {120},
year = {1995},
}

TY - JOUR
AU - Vrkoč, Ivo
TI - Weak averaging of stochastic evolution equations
JO - Mathematica Bohemica
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 120
IS - 1
SP - 91
EP - 111
AB - 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.
LA - eng
KW - stochastic evolution equations; averaging methods; weak convergence; stochastic evolution equations; averaging methods
UR - http://eudml.org/doc/247786
ER -

References

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  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. (1983) Zbl0538.60006MR0693792
  2. G. Da Prato J. Zabczyk, Stochastic equations in infinite dimensions, Cambridge University Press, Cambridge, 1992. (1992) MR1207136
  3. R. M. Dudley, Real analysis and probability, Wadsworth & Brook/Cole, Pacific Grove, 1989. (1989) Zbl0686.60001MR0982264
  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. (1964) 
  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. (1963) 
  6. P. 3. Xacьмuнcкuй, O пpинципe ycpeднeния для cтoxacтичecкиx диффepeнциaльныx ypaвнeний Итo, Kybernetika Ą (1968), 260-279. (1968) 
  7. B. Maslowski J. Seidler I. Vrkoč, An averaging principle for stochastic evolution equations II, Math. Bohem. 116 (1991), 191-224. (1991) MR1112004
  8. B. Maslowski J. Seidler I. Vrkoč, Integral continuity and stability for stochastic hyperbolic equations, Differential Integral Equations 6 (1993), 355-382. (1993) MR1195388
  9. J. Seidler, Da Prato-Zabczyk's maximal inequality revisited I, Math. Bohem. 118 (1993), 67-106. (1993) Zbl0785.35115MR1213834
  10. J. Seidler I. Vrkoč, An averaging principle for stochastic evolution equations, Čas. Pěst. Mat. 115 (1990), 240-263. (1990) MR1071056
  11. A. B. Cкopoxoд, Acимптoтичecкиe мeтoды тeopии cтoxacтичecкиx диффepeнциaльныx ypaвнeний, Hayкoвa Дyмкa, Kиeв, 1987. (1987) 
  12. I. Vrkoč, Extension of the averaging method to stochastic equations, Czechoslovak Math. J. 16 (91) (1966), 518-544. (1966) MR0205318

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