For additive functionals defined on a sequence of Markov chains that approximate a Markov process, we establish the convergence of functionals under the condition of local convergence of their characteristics (mathematical expectations).
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Yu. N. Kartashov and A. M. Kulik, Invariance Principle for Additive Functionals of Markov Chains, arXiv:0704.0508v1 (2007).
E. B. Dynkin, Markov Processes [in Russian], Fizmatgiz, Moscow (1963).
A. M. Kulyk, “Difference approximation of local times of multidimensional diffusions,” Teor. Imovir. Mat. Statyst., 78, 86–102 (2008).
A. M. Kulik, “Markov approximation of stable processes by random walks,” Theory Stochast. Process., 12(28), No. 1–2, 87–93 (2006).
A. M. Kulik, “A limit theorem for the number of sign changes for a sequence of one-dimensional diffusions,” Theory Stochast. Process., 14(30), No. 2, 79–92 (2008).
J. L. Doob, Classical Potential Theory and Its Probabilistic Counterpart, Springer, New York (2001).
P. Billingsley, Convergence of Probability Measures, Wiley, New York (1968).
E. B. Dynkin and A. A. Yushkevich, Theorems and Problems in Markov Processes [in Russian], Nauka, Moscow (1967).
A. M. Kulik, “Malliavin calculus for difference approximations of multidimensional diffusions: Truncated local limit theorem,” Ukr. Mat. Zh., 60, No. 3, 340–381 (2008).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 9, pp. 1208–1224, September, 2009.
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Kartashov, Y.N., Kulik, A.M. Convergence of difference additive functionals under local conditions on their characteristics. Ukr Math J 61, 1428–1447 (2009). https://doi.org/10.1007/s11253-010-0287-9
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DOI: https://doi.org/10.1007/s11253-010-0287-9