Motion in a Gaussian incompressible flow

Annals of Applied Probability

Volumn 7, Issue 1, 1997, Pages 229-264

  Komorowski, Tomasz ^a   Papanicolaou, George ^b  

^a MICHIGAN STATE UNIVERSITY   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Diffusion approximation; Mixing condition; Random field; Weak convergence

Indexed keywords

EID: 0031285164     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1034625261     Document Type: Article

References (33)

1. ADLER, R. J. (1981). Geometry of Random Fields. Wiley, New York.
2. ADLER, R. J. (1990). An Introduction to Continuity Extrema and Related Topics for General Gaussian Processes. IMS, Hayward, CA.
3. AVELLANEDA, M., ELLIOT, F., JR. and APELIAN, C. (1993). Trapping, percolation and anomalous diffusion of particles in a two-dimensional random field. J. Statist. Phys. 72 1227-1304.
4. AVELLANEDA, M. and MAJDA, A. J. (1991). An integral representation and bounds on the effective diffusivity in passive advection by laminar and turbulent flows. Comm. Math. Phys. 138 339-391.
5. BILLINGSLEY, P. (1968). Convergence of Probability Measures. Wiley, New York.
6. BROX, T. (1986). A one-dimensional process in a Wiener medium. Ann. Probab. 14 1206-1218.
7. CARMONA, R. and XU, L. (1997). Homogenization for time dependent two-dimensional incompressible Gaussian flows. Ann. Appl. Probab. 7 265-279.
8. CHORIN, A. (1994). Vorticity and Turbulence. Springer, Berlin.
9. DOUKHAN, P. (1994). Mixing. Properties and Examples. Springer, Berlin.
10. DUNFORD, N. and SCHWARTZ, J. T. (1988). Linear Operators 1. Wiley, New York.
11. FANNJIANG, A. and PAPANICOLAOU, G. C. (1994). Convection enhanced diffusion for periodic flows. SIAM J. Appl. Math. 54 333-408.
12. FANNJIANG, A. and PAPANICOLAOU, G. C. (1996). Convection enhanced diffusion for random flows. J. Statist. Phys. To appear.
13. FANNJIANG, A. and PAPANICOLAOU, G. C. (1996). Diffusion in turbulence. Probab. Theory Related Fields 105 279-334.
14. FOGUEL, S. (1969). Ergodic Theory of Markov Processes. Van Nostrand, New York.
15. GEMAM, D. and HOROWITZ, J. (1975). Random shifts which preserve measure. Proc. Amer. Math. Soc. 49 143-150.
16. ISICHENKO, M. B. (1992). Percolation, statistical topography and transport in random media. Rev. Modern Phys. 64 961-1043.
17. KAWAZU, K., TAMURA, Y. and TANAKA, H. (1989). Limit theorems for one-dimensional diffusions and random walks in random environments. Probab. Theory Related Fields 80 501-541.
18. KESTEN, H. and PAPANICOLAOU, G. C. (1979). A limit theorem for turbulent diffusion. Comm. Math. Phys. 65 97-128.
19. KHASMINSKII, R. Z. (1966). A limit theorem for solutions of differential equations with a random right-hand side. Theory Probab. Appl. 11 390-406.
20. KOMOROWSKI, T. (1996). Diffusion approximation for the advection of particles in a strongly turbulent random environment. Unpublished manuscript.
21. KOZLOV, S. M. (1985). The method of averaging and walks in inhomogeneous environments. Russian Math. Surveys 40 73-145.
22. KRAICHNAN, R. (1970). Diffusion in a random velocity field. Phys. Fluids 13 22-31.
23. MOLCHANOV, S. (1992). Lectures on random media. Ecole d'Eté de Probabilité de Saint-Flour XXII. Lecture Notes in Math. 1581 242-411. Springer, Berlin.
24. MONIN, A. S. and YAGLOM, A. M. (1971) (1975). Statistical Fluid Mechanics of Turbulence 1 and 2. MIT Press.
25. OESCHLAGER, K. (1988). Homogenization of a diffusion process in a divergence free random field. Ann. Probab. 16 1084-1126.
26. OSADA, H. (1982). Homogenization of diffusion processes with random stationary coefficients. Proceedings Fourth Japan-USSR Symposium on Probability Theory. Lecture Notes in Math. 1021 507-517. Springer, Berlin.
27. PAPANICOLAOU, G. C. and VARADHAN, S. R. S. (1982). Boundary value problems with rapidly oscillating random coefficients. Coll. Math. Soc. Janos Bolyai. 27 835-873. North-Holland, Amsterdam.
28. PORT, S. C. and STONE, C. (1976). Random measures and their application to motion in an incompressible fluid. J. Appl. Probab. 13 499-506.
29. ROZANOV, YU. A. (1969). Stationary Random Processes. Holden-Day, San Francisco.
30. SINAI, Y. G. (1982). The limiting behavior of a one-dimensional walk in a random medium. Theory Probab. Appl. 27 256-268.
31. STANISIŚ, M. M. (1988). The Mathematical Theory of Turbulence, 2nd ed. Springer, Berlin.
32. STONE, C. J. (1963). Weak convergence of stochastic processes defined on semi-infinite time intervals. Proc. Amer. Math. Soc. 14 694-696.
33. STROOK, D. and VARADHAN, S. R. S. (1979). Multidimensional Diffusion Processes. Springer, Berlin.