Abstract:
This is the continuation of the papers [8], [9]. In [9] some rough limit theorems were deduced from the estimates of [8]. These theorems are analogous to the limit theorems for the sums of independent random variables concerning «very large» deviations of order √n. In the present paper rough limit theorems for some other classes of families of Markov processes are derived from the estimates of [8] (slighthly modified); some of them are analogous to limit theorems concerning «not very large» deviations (those of order o(√n) for the sums of independent random variables.
Citation:
A. D. Wentzell, “Rough limit theorems on large deviations for Markov stochastic processes. III”, Teor. Veroyatnost. i Primenen., 24:4 (1979), 673–691; Theory Probab. Appl., 24:4 (1980), 675–692
This publication is cited in the following 8 articles:
Paul Dupuis, Dane Johnson, “Moderate deviations-based importance sampling for stochastic recursive equations”, Adv. Appl. Probab., 49:4 (2017), 981
V. I. Piterbarg, V. R. Fatalov, “The Laplace method for probability measures in Banach spaces”, Russian Math. Surveys, 50:6 (1995), 1151–1239
B�lint T�th, “Phase transition in an interacting Bose system. An application of the theory of Ventsel' and Freidlin”, J Stat Phys, 61:3-4 (1990), 749
Ph. Blanchard, M. Sirugue, “Large deviations from classical paths. Hamiltonian flows as classical limits of quantum flows”, Commun.Math. Phys., 101:2 (1985), 173
P. Blanchard, P. Combe, M. Sirugue, M. Sirugue-Collin, Lecture Notes in Mathematics, 1136, Quantum Probability and Applications II, 1985, 104
A. A. Borovkov, “Boundary-value problems, the invariance principle, and large deviations”, Russian Math. Surveys, 38:4 (1983), 259–290
V. V. Godovančuk, A. P. Korostelev, “Conditions for the local convergence of recursive stochastic procedures”, Theory Probab. Appl., 28:1 (1984), 142–149
A. D. Wentzel', “Rough limit theorems on large deviations for Markov stochastic processes. IV”, Theory Probab. Appl., 27:2 (1983), 209–227