Abstract
A diffusion process with a drift b(x) and small diffusion sooner or later reaches the boundary of a region containing a stable position of equilibrium of the dynamical system x(t)=b(xt). The first exit point belongs to a small part of the boundary (see [1, 2]). An estimate of the order of the size of this part is given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
A. D. Venttsel' and M. I. Freidlin, “Small random oscillations of a dynamical system with a stable position of equilibrium,” Dokl. Akad. Nauk SSSR,187, No. 3, 506–509 (1969).
A. D. Venttsel' and M. I. Freidlin, “On small random oscillations of dynamical systems,” Usp. Mat. Nauk,25, No. 1, 3–55 (1970).
J. L. Doob, Stochastic Processes, Wiley, New York (1953).
M. I. Freidlin, “An action functional for a class of random processes,” Teor. Veroyatn. Ee Primen.,17, No. 3, 536–541 (1972).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 22, No. 3, pp. 411–420, September, 1977.
Rights and permissions
About this article
Cite this article
Venttsel', A.D. The first boundary exit point of a diffusion process with small diffusion. Mathematical Notes of the Academy of Sciences of the USSR 22, 720–725 (1977). https://doi.org/10.1007/BF02412502
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02412502