An averaging principle for stochastic evolution equations. II.

Bohdan Maslowski; Jan Seidler; Ivo Vrkoč

Mathematica Bohemica (1991)

  • Volume: 116, Issue: 2, page 191-224
  • ISSN: 0862-7959

Abstract

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In the present paper integral continuity theorems for solutions of stochastic evolution equations of parabolic type on unbounded time intervals are established. For this purpose, the asymptotic stability of stochastic partial differential equations is investigated, the results obtained being of independent interest. Stochastic evolution equations are treated as equations in Hilbert spaces within the framework of the semigroup approach.

How to cite

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Maslowski, Bohdan, Seidler, Jan, and Vrkoč, Ivo. "An averaging principle for stochastic evolution equations. II.." Mathematica Bohemica 116.2 (1991): 191-224. <http://eudml.org/doc/29291>.

@article{Maslowski1991,
abstract = {In the present paper integral continuity theorems for solutions of stochastic evolution equations of parabolic type on unbounded time intervals are established. For this purpose, the asymptotic stability of stochastic partial differential equations is investigated, the results obtained being of independent interest. Stochastic evolution equations are treated as equations in Hilbert spaces within the framework of the semigroup approach.},
author = {Maslowski, Bohdan, Seidler, Jan, Vrkoč, Ivo},
journal = {Mathematica Bohemica},
keywords = {stochastic evolution equations; integral continuity theorems; asymptotic stability; stochastic partial differential equations; semigroup approach; stochastic evolution equations; asymptotic stability; stochastic partial differential equations; semigroup approach},
language = {eng},
number = {2},
pages = {191-224},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An averaging principle for stochastic evolution equations. II.},
url = {http://eudml.org/doc/29291},
volume = {116},
year = {1991},
}

TY - JOUR
AU - Maslowski, Bohdan
AU - Seidler, Jan
AU - Vrkoč, Ivo
TI - An averaging principle for stochastic evolution equations. II.
JO - Mathematica Bohemica
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 116
IS - 2
SP - 191
EP - 224
AB - In the present paper integral continuity theorems for solutions of stochastic evolution equations of parabolic type on unbounded time intervals are established. For this purpose, the asymptotic stability of stochastic partial differential equations is investigated, the results obtained being of independent interest. Stochastic evolution equations are treated as equations in Hilbert spaces within the framework of the semigroup approach.
LA - eng
KW - stochastic evolution equations; integral continuity theorems; asymptotic stability; stochastic partial differential equations; semigroup approach; stochastic evolution equations; asymptotic stability; stochastic partial differential equations; semigroup approach
UR - http://eudml.org/doc/29291
ER -

References

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  1. A. V. Balakrishnan, Applied functional analysis, Springer-Verlag, New York-Heidelberg- Berlin 1976. (1976) Zbl0333.93051MR0470699
  2. P. L. Butzer H. Berens, Semi-groups of operators and approximation, Springer-Verlag, Berlin-Heidelberg-New York 1967. (1967) MR0230022
  3. N. Dunford J. T. Schwartz, Linear operators, Part II, Interscience, New York-London 1963. (1963) MR0188745
  4. A. H. Филатов, Методы усреднения в дифференциальных и интегродифференциальных уравнениях, Фан, Tашкент 1971. (1971) Zbl1168.35423
  5. A. Friedman, Stochastic differential equations and applications, vol. 1. Academic Press, New York 1975. (1975) Zbl0323.60056MR0494490
  6. T. Funaki, 10.1017/S0027763000020298, Nagoya Math. J. 89 (1983), 129-193. (1983) Zbl0531.60095MR0692348DOI10.1017/S0027763000020298
  7. A. Ichikawa, 10.1016/0022-247X(82)90041-5, J. Math. Anal. Appl. 90 (1982), 12-44. (1982) Zbl0497.93055MR0680861DOI10.1016/0022-247X(82)90041-5
  8. A. Ichikawa, 10.1080/17442508408833293, Stochastics 12 (1984), 1 - 39. (1984) Zbl0538.60068MR0738933DOI10.1080/17442508408833293
  9. B. Maslowski, On some stability properties of stochastic differential equations of Itó's type, Časopis pěst. mat. 111 (1986), 404-423. (1986) Zbl0625.60066MR0871716
  10. J. Seidler I. Vrkoč, An averaging principle for stochastic evolution equations, Časopis pěst. mat. 115 (1990), 240-263. (1990) MR1071056
  11. I. Vrkoč, Extension of the averaging method to stochastic equations, Czechoslovak Math. J. 16 (91) (1966), 518-544. (1966) MR0205318

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