Abstract
We prove an existence theorem and establish the property of stochastic stability for processes determined by the Poisson stochastic differential equations with delay.
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REFERENCES
K. Itô and M. Nisio, “On stationary solutions of a stochastic differential equation,” Kyoto J. Math., 4, 1–75 (1964).
W. Fleming and M. Nisio, “On the existence of optimal stochastic control,” J. Math. Mech., 15, 777–794 (1966).
J. Doob, Stochastic Processes, Wiley, New York (1953).
E. Dynkin, Markov Processes, Springer, Berlin (1965).
H. Kushner, “On the stability of the processes defined by stochastic difference-differential equations,” J. Differential Equat., 424–443 (1968).
V. B. Kolmanovskii, “On stability of stochastic schemes with delay,” Probl. Peredachi Inform., 5, No. 4, 59–67 (1969).
E. F. Tsar'kov, “Mean-square asymptotic exponential stability of the trivial solution of a stochastic differential equation with delay,” Teor. Ver. Primen., 21, 850–875 (1976).
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Svishchuk, A.V., Svishchuk, M.Y. Stochastic Stability of Processes Determined by Poisson Differential Equations with Delay. Ukrainian Mathematical Journal 54, 511–518 (2002). https://doi.org/10.1023/A:1020529903994
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DOI: https://doi.org/10.1023/A:1020529903994