Stochastic perturbations to conservative dynamical systems on the plane. II. Recurrency conditions
HTML articles powered by AMS MathViewer
- by G. Wolansky
- Trans. Amer. Math. Soc. 309 (1988), 641-657
- DOI: https://doi.org/10.1090/S0002-9947-1988-0961605-1
- PDF | Request permission
Abstract:
We consider a conservative system on the plane, subjected to a perturbation. The above perturbation is composed of a deterministic part and a random (white noise) part. We discuss the conditions under which there exists a unique, finite invariant measure to the perturbed system, and the weak compactness of the above measures for small enough perturbation’s parameter.References
- R. N. Bhattacharya, Criteria for recurrence and existence of invariant measures for multidimensional diffusions, Ann. Probab. 6 (1978), no. 4, 541–553. MR 0494525, DOI 10.1214/aop/1176995476
- M. I. Freidlin and A. D. Wentzell, Random perturbations of dynamical systems, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 260, Springer-Verlag, New York, 1984. Translated from the Russian by Joseph Szücs. MR 722136, DOI 10.1007/978-1-4684-0176-9 A. Friedman, Stochastic differential equations and application, Vol. I, Academic Press, 1976.
- R. Z. Has′minskiĭ, Ergodic properties of recurrent diffusion processes and stabilization of the solution of the Cauchy problem for parabolic equations, Teor. Verojatnost. i Primenen. 5 (1960), 196–214 (Russian, with English summary). MR 0133871
- G. Wolansky, Stochastic perturbations to conservative dynamical systems on the plane. I. Convergence of invariant distributions, Trans. Amer. Math. Soc. 309 (1988), no. 2, 621–639. MR 961604, DOI 10.1090/S0002-9947-1988-0961604-X
Bibliographic Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 309 (1988), 641-657
- MSC: Primary 35R60; Secondary 58F11, 60J60, 93E03
- DOI: https://doi.org/10.1090/S0002-9947-1988-0961605-1
- MathSciNet review: 961605