Almost sure and moment stability of stochastic partial differential equations

• Autorzy: Kwiecińska A. A.
• Języki publikacji: EN

Abstrakty

EN

We study the almost sure and moment stability of a class of stochastic partial differential equations and we present an infinite-dimensional version of a theorem proved for stochastic ordinary differential equations by Arnold, Oeljeklaus and Pardoux. We also investigate how adding a term with white noise influences the stability of a deterministic system. The outcome is quite surprising. It turns out that regardless whether the deterministic system was stable or unstable, after adding a term with sufficiently large noise, it becomes pathwise exponentially stable and unstable in the p-th mean for p >1.

Słowa kluczowe

EN

stochastic partial differential equation; almost sure stability; moment stability; deterministic partial differential equation; stabilization by noise; estabilization by noise

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2001
• Tom: Vol. 21, Fasc. 2
• Strony: 405--415
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Kwiecińska A. A.

• Institute of Mathematics Polish Academy of Sciences, ul Śniadeckich 8, 00-950 Warszawa, Poland

Bibliografia

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• [2] L. Arnold, E. Oeljeklaus and E. Pardoux, Almost sure and moment stability for linear Itô equations, in Lyapunov Exponents, Lecture Notes in Math, 118ó, L. Arnold and V. Wihstutz (Eds.), Springer, 1984, pp. 129 459.
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• [6] A. A. Kwiecińska, Stabilization of partial differential equations by noise. Stochastic Process. Appl. 79 (1999), pp. 179-184.
• [7] A. A, Kwiecińska, Stabilization of evolution equations by noise, Proc. Amer, Math. Soc. (to appear).
• [8] O. A. Ladyzhenskaya, The boundary value problems of mathematical physics (in Russian), Nauka, Moscow 1973 (English translation: Springer, 1985).
• [9] R. Temam, Infinite-dimensional dynamical systems in mechanics and physics, Appl. Math. Sci, 68, Springer, New York 1997, second edition.