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Small Random perturbation of dynamical systems with reflecting boundary

Published online by Cambridge University Press:  22 January 2016

Robert F. Anderson
Affiliation:
University of Minnesota
Steven Orey
Affiliation:
University of Minnesota
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Consider a diffusion process in Rd satisfying the stochastic differential equation

.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[1] Aronson, D. G., The fundamental solution of a linear parabolic equation containing a small parameter, III. J. Math., 3 (1959), 580619.Google Scholar
[2] Friedman, A., Small random perturbation of dynamical systems and applications to parabolic equation, Ind. U. Math. J., 34 (1974), 533553, 24 (1975), 903.Google Scholar
[3] Skorokhod, A. V., Stochastic equations for diffusions in a bounded region, Theor. of Prob. and its Appl., 6 (1961), 264274.CrossRefGoogle Scholar
[4] Stroock, D. W. and Varadhan, S. R. S., Diffusions with boundary conditions. Comm. Pure. Appl. Math., 34 (1971), 147225.Google Scholar
[5] Varadhan, S. R. S., On the behavior of the fundamental solution of the heat equation with variable coefficients. Comm. Pure Appl. Math., 20 (1967), 431455.Google Scholar
[6] Varadhan, S. R. S., Diffusion processes in a small time interval, Comm. Pure Appl. Math., 20 (1967), 659685.Google Scholar
[7] Ventcel, A. D. and Freidlin, M. J., On small random perturbations of dynamical systems, Russ. Math. Surveys, 25 (1970), No. 1, 156 (Uspakhi Math. Nauk, 28 (1970), No. 1, 355).Google Scholar
[8] Watanabe, S., On stochastic differential equations for multidimensional diffusion processes with boundary, I, II, J. Math. Kyoto U., 11 (1971), 169180, 545551.Google Scholar