Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-30T15:32:57.150Z Has data issue: false hasContentIssue false
  • English
  • Français

Small Random perturbation of dynamical systems with reflecting boundary

Published online by Cambridge University Press:  22 January 2016

Robert F. Anderson  and
Steven Orey
Robert F. Anderson
Affiliation:
University of Minnesota
Steven Orey
Affiliation:
University of Minnesota
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Consider a diffusion process in Rd satisfying the stochastic differential equation

.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 60 , February 1976 , pp. 189 - 216
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), 580–619.Google Scholar
[2] Friedman, A., Small random perturbation of dynamical systems and applications to parabolic equation, Ind. U. Math. J., 34 (1974), 533–553, 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), 264–274.CrossRefGoogle Scholar
[4] Stroock, D. W. and Varadhan, S. R. S., Diffusions with boundary conditions. Comm. Pure. Appl. Math., 34 (1971), 147–225.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), 431–455.Google Scholar
[6] Varadhan, S. R. S., Diffusion processes in a small time interval, Comm. Pure Appl. Math., 20 (1967), 659–685.Google Scholar
[7] Ventcel, A. D. and Freidlin, M. J., On small random perturbations of dynamical systems, Russ. Math. Surveys, 25 (1970), No. 1, 1–56 (Uspakhi Math. Nauk, 28 (1970), No. 1, 3–55).Google Scholar
[8] Watanabe, S., On stochastic differential equations for multidimensional diffusion processes with boundary, I, II, J. Math. Kyoto U., 11 (1971), 169–180, 545–551.Google Scholar