On nonuniform dichotomy for stochastic skew-evolution semiflows in Hilbert spaces

Diana Stoica; Mihail Megan

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 4, page 879-887
  • ISSN: 0011-4642

Abstract

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In this paper we study a general concept of nonuniform exponential dichotomy in mean square for stochastic skew-evolution semiflows in Hilbert spaces. We obtain a variant for the stochastic case of some well-known results, of the deterministic case, due to R. Datko: Uniform asymptotic stability of evolutionary processes in a Banach space, SIAM J. Math. Anal., 3(1972), 428–445. Our approach is based on the extension of some techniques used in the deterministic case for the study of asymptotic behavior of skew-evolution semiflows in Banach spaces.

How to cite

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Stoica, Diana, and Megan, Mihail. "On nonuniform dichotomy for stochastic skew-evolution semiflows in Hilbert spaces." Czechoslovak Mathematical Journal 62.4 (2012): 879-887. <http://eudml.org/doc/247145>.

@article{Stoica2012,
abstract = {In this paper we study a general concept of nonuniform exponential dichotomy in mean square for stochastic skew-evolution semiflows in Hilbert spaces. We obtain a variant for the stochastic case of some well-known results, of the deterministic case, due to R. Datko: Uniform asymptotic stability of evolutionary processes in a Banach space, SIAM J. Math. Anal., 3(1972), 428–445. Our approach is based on the extension of some techniques used in the deterministic case for the study of asymptotic behavior of skew-evolution semiflows in Banach spaces.},
author = {Stoica, Diana, Megan, Mihail},
journal = {Czechoslovak Mathematical Journal},
keywords = {stochastic skew-evolution semiflow; nonuniform exponential dichotomy in mean square; stochastic skew-evolution semiflow; nonuniform exponential dichotomy; mean square},
language = {eng},
number = {4},
pages = {879-887},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On nonuniform dichotomy for stochastic skew-evolution semiflows in Hilbert spaces},
url = {http://eudml.org/doc/247145},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Stoica, Diana
AU - Megan, Mihail
TI - On nonuniform dichotomy for stochastic skew-evolution semiflows in Hilbert spaces
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 4
SP - 879
EP - 887
AB - In this paper we study a general concept of nonuniform exponential dichotomy in mean square for stochastic skew-evolution semiflows in Hilbert spaces. We obtain a variant for the stochastic case of some well-known results, of the deterministic case, due to R. Datko: Uniform asymptotic stability of evolutionary processes in a Banach space, SIAM J. Math. Anal., 3(1972), 428–445. Our approach is based on the extension of some techniques used in the deterministic case for the study of asymptotic behavior of skew-evolution semiflows in Banach spaces.
LA - eng
KW - stochastic skew-evolution semiflow; nonuniform exponential dichotomy in mean square; stochastic skew-evolution semiflow; nonuniform exponential dichotomy; mean square
UR - http://eudml.org/doc/247145
ER -

References

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  15. Stoica, C., Megan, M., Nonuniform behaviors for skew-evolution semiflows in Banach spaces, Operator theory live. Proceedings of the 22nd international conference on operator theory, Timişoara, Romania, July 3-8, 2008. Bucharest: The Theta Foundation. Theta Series in Advanced Mathematics 12 (2010), 203-211. (2010) MR2731875
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