|
Diffusion approximation of evolutionary systems with equilibrium in asymptotic split phase space
Author(s):
Vladimir
S.
Korolyuk;
Nikolaos
Limnios
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 70
(2004).
Journal:
Theor. Probability and Math. Statist.
No. 70
(2005),
71-82.
MSC (2000):
Primary 60J55, 60J75, 60F17
Posted:
August 26, 2005
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper we consider an additive functional of a Markov process with locally independent increments switched by a Markov process. For this functional, we obtain nonhomogeneous diffusion approximation results without balance condition on the drift parameter. A more general diffusion approximation result is obtained in the case of an asymptotic split phase space of the switching Markov process.
References:
-
- 1.
- V. V. Anisimov, Application of limit theorems for switching processes, Cybernetics 6 (1978), 917-929. MR 0523681 (80e:60029)
- 2.
- V. V. Anisimov, Switching processes: averaging principle, diffusion approximation and applications, Acta Aplicandae Mathematica 40 (1995), 95-141. MR 1338444 (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. MR 1772938 (2001i:60147)
- 4.
- A. Bensoussan, J.-L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, 1978. MR 0503330 (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. MR 0476129 (57:15707)
- 6.
- M. H. A. Davis, Markov Models and Optimization, Chapman & Hall, 1993. MR 1283589 (96b:90002)
- 7.
- S. N. Ethier and T. G. Kurtz, Markov Processes. Characterization and Convergence, J. Wiley, 1986. MR 0838085 (88a:60130)
- 8.
- M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical Systems, 2nd edition, Springer, New York, 1998. MR 1652127 (99h:60128)
- 9.
- I. I. Gihman and A. V. Skorokhod, Theory of Stochastic Processes, vol. 1, Springer, Berlin, 1974. MR 0346882 (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. MR 1100751
- 11.
- D. L. Iglehart, Diffusion approximations in collective risk theory, J. Appl. Prob. 6 (1969), 285-292. MR 0256442 (41:1098)
- 12.
- V. S. Korolyuk and V. V. Korolyuk, Stochastic Models of Systems, Kluwer, 1999. MR 1753470 (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. MR 1793643 (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. MR 1793768
- 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. MR 1826144
- 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. MR 1783480 (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. MR 1413300 (98g:60116)
- 19.
- H. J. Kushner, Weak Convergence Methods and Singular Perturbed Stochastic Control and Filtering Problems, Birkhäuser, Boston, 1990. MR 1102242 (92d:93003)
- 20.
- N. Limnios and G. Oprisan, Semi-Markov Processes and Reliability, Birkhäuser, Boston, 2001. MR 1843923 (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. MR 0808207 (87f:60049)
- 22.
- L. C. G. Rogers and D. Williams, Diffusions, Markov Processes, and Martingales, vols. 1, 2, Wiley, Chichester, U.K., 1994. MR 1331599 (96h:60116)
- 23.
- A. V. Skorokhod, Asymptotic Methods in the Theory of Stochastic Differential Equations, AMS, Providence, 1989. MR 1020057 (90i:60038)
- 24.
- D. W. Stroock and S. R. S. Varadhan, Multidimensional Diffusion Processes, Springer-Verlag, Berlin, 1979. MR 0532498 (81f:60108)
- 25.
- G. G. Yin and Q. Zhang, Continuous-Time Markov Chains and Applications, Springer, New York, 1998. MR 1488963 (2000a:60142)
Similar Articles:
Retrieve articles in Theory of Probability and Mathematical Statistics
with MSC
(2000):
60J55, 60J75, 60F17
Retrieve articles in all Journals with MSC
(2000):
60J55, 60J75, 60F17
Additional Information:
Vladimir
S.
Korolyuk
Affiliation:
Ukrainian National Academy of Sciences, Ukraine
Nikolaos
Limnios
Affiliation:
Université de Technologie de Compiègne, France
DOI:
10.1090/S0094-9000-05-00632-0
PII:
S 0094-9000(05)00632-0
Keywords:
Diffusion approximation,
additive functional,
asymptotic split phase space,
Markov process with locally independent increments,
nonhomogeneous diffusion
Received by editor(s):
20/JAN/2004
Posted:
August 26, 2005
Additional Notes:
This work is partially supported by INTAS project # 9900016.
Copyright of article:
Copyright
2005,
American Mathematical Society
|
Comments: webmaster@ams.org