Diffusion approximation for slow motion in fully coupled averaging

Probability Theory and Related Fields

Volumn 129, Issue 2, 2004, Pages 157-181

  Bakhtin, Victor ^a   Kifer, Yuri ^b  

^a BELARUSIAN STATE UNIVERSITY   (Belarus)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

Averaging; Diffusion; Limit theorems; Stochastic differential equations

Indexed keywords

EID: 2942597464     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-003-0326-7     Document Type: Article

References (21)

1. Bakhtin, V.I.: Cramér asymptotics in a system with slow and fast Markovian motions. Theory Probab. Appl. 44, 1-17 (1999)
2. Bakhtin, V.I.: Asymptotics of superregular perturbations of fiber ergodic semigroups. Stochastics and Stochastics Reports 75, 295-318 (2003)
3. Bakhtin, V.I.: Cramér asymptotics in a system with fast and slow motions. Stochastics and Stochastics Reports 75, 319-341 (2003)
4. Billingsley, P.: Convergence of Probability Measures. 2nd (ed.), J. Wiley, New York, 1999
5. Berkes, I., Philipp, W.: Approximation theorems for independent and weakly dependent random vectors. Ann. Probab. 7, 29-54 (1979)
6. Doukhan, P.: Mixing. Springer-Verlag, New York, 1994
7. Dehling, H., Philipp, W.: Empirical process techniques for dependent data. In: Empirical Process Techniques for Dependent Data H.G. Dehling, T. Mikosch, M. Sorensen, (eds.), Birkhäuser, 2002
8. Dudley, R.M., Philipp, W.: Invariance principles for sums of Banach space valued random elements and empirical processes. Z. Wahrscheinlichkeitstheor. Verw. Geb. 62, 509-552 (1983)
9. Freidlin, M.I.: Functional Integration and Partial Differential Equations. Princeton Univ. Press, Princeton, 1985
10. Freidlin, M.I.,Wentzell, A.D.: Random Perturbations of Dynamical Systems. 2nd ed., Springer-Verlag, New York, 1998
11. Gray, A.: Tubes, Addison-Wesley, Redwood City, Ca., 1990
12. Hasselmann, K.: Stochastic climate models. Part I. Theory. Tellus 28,473-485 (1976)
13. Hsu, E.P.: Stochastic analysis on manifolds. American Math. Soc., Providence, RI, 2002
14. Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes. North-Holland, Amsterdam (Kodansha Ltd. Tokyo), 1981
15. Khasminskii, R.Z.: On stochastic processes defined by differential equations with a small parameter. Th. Probab. Appl. 11, 211-228 (1966)
16. Kifer, Y.: Averaging and climate models. Stochastic Climate Models, Progress in Probability 49 Birkhäuser, 2001
17. 2 diffusion approximation for slow motion in averaging. Stochastics and Dynamics 3, 213-246 (2003)
18. Kunita, H.: Stochastic Flows and Stochastic Differential Equations. Cambridge Univ. Press, Cambridge, 1990
19. Monrad, D., Philipp, W.: Nearby variables with nearby conditional laws and a strong approximation theorem for Hilbert space valued martingales. Probab. Th. Rel. Fields 88, 381-404 (1991)
20. Philipp, W.: The profound impact of Paul Erdoes on probability limit theory - a personal account. In: "Paul Erdös and his Mathematics", I, pp. 549-566, Budapest, 2002
21. Philipp, W., Stout, W.: Almost Sure Invariance Principles for Partial Sums of Weakly Dependent Random Variables. Mem. Amer. Math. Soc., 161 Providence, R.I., 1975