Diffusion approximation of evolutionary systems with equilibrium in asymptotic split phase space

Theory of Probability and Mathematical Statistics

Volumn 70, Issue , 2005, Pages 71-82

  Korolyuk, Vladimir S ^a   Limnios, Nikolaos ^b  

^a INSTITUTE OF HYDROBIOLOGY   (Ukraine)

^b UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

Additive functional; Asymptotic split phase space; Diffusion approximation; Markov process with locally independent increments; Nonhomogeneous diffusion

Indexed keywords

EID: 85009772387     PISSN: 00949000     EISSN: 15477363     Source Type: Journal    
DOI: 10.1090/S0094-9000-05-00632-0     Document Type: Article

References (25)

1. V. V. Anisimov, Application of limit theorems for switching processes, Cybernetics 6 (1978), 917–929. MR0523681 (80e:60029)
2. V. V. Anisimov, Switching processes: averaging principle, diffusion approximation and applications, Acta Aplicandae Mathematica 40 (1995), 95–141. MR1338444 (96j:60032)
3. V. V. Anisimov, Diffusion approximation for processes with semi-Markov switchies, Semi-Markov Processes and Applications (J. Janssen and N. Limnios, eds.), Kluwer, Dordrecht, 1999, pp. 77–101. MR1772938 (2001i:60147)
4. A. Bensoussan, J.-L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, 1978. MR0503330 (82h:35001)
5. G. L. Blankenship and G. C. Papanicolaou, Stability and control of stochastic systems with wide band noise disturbances I, SIAM J. Appl. Math. 34 (1978), 437–476. MR0476129 (57:15707)
6. M. H. A. Davis, Markov Models and Optimization, Chapman & Hall, 1993. MR1283589 (96b:90002)
7. S. N. Ethier and T. G. Kurtz, Markov Processes. Characterization and Convergence, J. Wiley, 1986. MR0838085 (88a:60130)
8. M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical Systems, 2nd edition, Springer, New York, 1998. MR1652127 (99h:60128)
9. I. I. Gihman and A. V. Skorokhod, Theory of Stochastic Processes, vol. 1, Springer, Berlin, 1974. MR0346882 (49:11603)
10. P. W. Glynn, Diffusion approximation, Handbook in Operations Research and Management Science (D. P. Heyman and M. J. Sobel, eds.), vol. 2 (Stochastic Models), North-Holland, Amsterdam, 1990, pp. 145–198. MR1100751
11. D. L. Iglehart, Diffusion approximations in collective risk theory, J. Appl. Prob. 6 (1969), 285–292. MR0256442 (41:1098)
12. V. S. Korolyuk and V. V. Korolyuk, Stochastic Models of Systems, Kluwer, 1999. MR1753470 (2002b:60169)
13. V. S. Korolyuk and N. Limnios, A singular perturbation approach for Liptser’s functional limit theorem and some extensions, Theory Probab. and Math. Statist. 58 (1998), 83–88. MR1793643 (2001g:60176)
14. V. S. Korolyuk and N. Limnios, Diffusion approximation of integral functionals in merging and averaging scheme, Theor. Probab. and Math. Statist. 59 (1999), 91–98. MR1793768
15. V. S. Korolyuk and N. Limnios, Diffusion approximation of integral functionals in double merging and averaging scheme, Theory Probab. and Math. Statist. 60 (2000), 87–94. MR1826144
16. V. S. Korolyuk and N. Limnios, Evolutionary systems in an asymptotic split state space, Recent Advances in Reliability Theory: Methodology, Practice, and Inference (N. Limnios and M. Nikulin, eds.), Birkhäuser, Boston, 2000, pp. 145–161. MR1783480 (2001e:60071)
17. V. S. Korolyuk and N. Limnios, Average and diffusion approximation of evolutionary systems in an asymptotic split state space. (to appear)
18. V. S. Korolyuk and A. Swishchuk, Evolution of Systems in Random Media, CRC Press, 1995. MR1413300 (98g:60116)
19. H. J. Kushner, Weak Convergence Methods and Singular Perturbed Stochastic Control and Filtering Problems, Birkhäuser, Boston, 1990. MR1102242 (92d:93003)
20. N. Limnios and G. Oprişan, Semi-Markov Processes and Reliability, Birkhäuser, Boston, 2001. MR1843923 (2002i:60161)
21. R. Sh. Liptser, On a functional limit theorem for finite state space Markov processes, Steklov Seminar on Statistics and Control of Stochastic Processes, Optimization Software, New York, 1984, pp. 305–316. MR0808207 (87f:60049)
22. L. C. G. Rogers and D. Williams, Diffusions, Markov Processes, and Martingales, vols. 1, 2, Wiley, Chichester, U.K., 1994. MR1331599 (96h:60116)
23. A. V. Skorokhod, Asymptotic Methods in the Theory of Stochastic Differential Equations, AMS, Providence, 1989. MR1020057 (90i:60038)
24. D. W. Stroock and S. R. S. Varadhan, Multidimensional Diffusion Processes, Springer-Verlag, Berlin, 1979. MR0532498 (81f:60108)
25. G. G. Yin and Q. Zhang, Continuous-Time Markov Chains and Applications, Springer, New York, 1998. MR1488963 (2000a:60142)