Abstract
We consider an evolutionary system switched by a semi-Markov process. For this system, we obtain an inhomogeneous diffusion approximation results where the initial process is compensated by the averaging function in the average approximation scheme.
Similar content being viewed by others
REFERENCES
A. V. Skorokhod, Asymptotic Theory of Stochastic Differential Equations, American Mathematical Society, Providence, RI (1981).
K. Sobsczyk, Stochastic Differential Equations, Kluwer, Dordrecht (1991).
V. S. Korolyuk and A. Swishchuk, Evolution of Systems in Random Media, CRC Press (1995).
V. S. Korolyuk and V. V. Korolyuk, Stochastic Models of Systems, Kluwer, Dordrecht (1999).
V. S. Korolyuk and N. Limnios, “Average and diffusion approximation for evolutionary systems in an asymptotic split phase space,” Ann. Appl. Probab., 14(1), 489–516 (2004).
V. S. Korolyuk and N. Limnios, “Diffusion approximation of evolutionary systems with equilibrium in asymptotic split phase space,” Theory Probab. Math. Statist., 69 (2002).
V. S. Korolyuk and N. Limnios, “Poisson approximation of homogeneous stochastic additive functionals with semi-Markov switching,” Theory Probab. Math. Statist., 64, 75–84 (2002).
V. S. Korolyuk and N. Limnios, “Poisson approximation of increment processes with Markov switching, ” Theory Probab. Appl., 49(4), 1–18 (2004).
Author information
Authors and Affiliations
Additional information
__________
Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 9, pp. 1253–1260, September, 2005.
Rights and permissions
About this article
Cite this article
Korolyuk, V.S., Limnios, N. Diffusion Approximation with Equilibrium for Evolutionary Systems Switched by Semi-Markov Processes. Ukr Math J 57, 1466–1476 (2005). https://doi.org/10.1007/s11253-006-0007-7
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11253-006-0007-7