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structural stability; invariant measure of a stochastic differential equation; Lyapunov type function; molecular rotation model
Stability of an invariant measure of stochastic differential equation with respect to bounded pertubations of its coefficients is investigated. The results as well as some earlier author's results on Liapunov type stability of the invariant measure are applied to a system describing molecular rotation.
[1] J. McConell: Stochastic differential equation study of nuclear magnetic relaxation by spinrotational interactions. Physica 111A (1982), 85-113. DOI 10.1016/0378-4371(82)90084-X
[2] I. I. Gikhman A. V. Skorokhod: Стохастические дифференциальные уравнения. Naukova Dumka, Kijev 1968.
[3] Kiyomasha Narita: Remarks on nonexplosion theorem for stochastic differential equations. Kodai Math. J. 5 (1982), 3, 395-401. DOI 10.2996/kmj/1138036606 | MR 0684796
[4] B. Maslowski: An application of l-condition in the theory of stochastic differential equations. Časopis pěst. mat. 123 (1987), 296-307 MR 0905976
[5] B. Maslowski: Weak stability of a certain class of Markov processes and applications to nonsingular stochastic differential equations. to appear. MR 0944482 | Zbl 0644.60050
[6] B. Maslowski: Stability of solutions of stochastic differential equations. (Czech), Thesis, Math. Institute of Czech. Academy of Sciences, 1985.
[7] A. Lasota: Statistical stability of deterministic systems. Proc. of the Internat. Conf. held in Würzburg, FRG, 1982; Lecture Notes in Math. 1017, 386-419. DOI 10.1007/BFb0103267 | MR 0726599
[8] R. Z. Khasminskii: Устойчивсоть систем диффернциальных уравнений при случайных возмущениях их параметров. Nauka, Moscow 1969.
[9] M. Zakai: A Liapunov criterion for the existence of stationary probability distributions for systems perturbed by noise. SIAM J. Control 7 (1969), 390-397. DOI 10.1137/0307028 | MR 0263176
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