This is a preview of subscription content, log in via an institution to check access.
Literature cited
F. Spitzer, Principles of Random Walks [Russian translation], Mir, Moscow (1969).
T. M. Mirzoeva, “On the asymptotic behavior of the number of intersections of an irreversible walk with some level,” in: Random Processes in Problems of Mathematical Physics [in Russian], Inst. Mat. Acad. Sci. Ukr. SSR, Kiev (1979), pp. 107–112.
T. M. Mirzoeva and N. I. Portenko, “Limiting distributions of functionals of irreversible random walks, becoming reversible in the limit,” in: Selected Problems in the Theory of Random Processes [in Russian], Inst. Mat. Acad. Sci. Ukr. SSR, Kiev (1984), pp. 79–96.
N. I. Portenko, “The asymptotic behavior of the potential kernel of a one-dimensional irreversible random walk,” Ukr. Mat. Zh.,26, No. 1, 25–36 (1974).
I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes [in Russian], Nauka, Moscow (1977).
E. B. Dynkin, Markov Processes [in Russian], Fizmatgiz, Moscow (1963).
V. M. Surenkov, “Final probabilities of ergodic Markov processes,” Lecture Notes in Math., Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, No. 1021 (1982), pp. 655–665.
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 37, No. 1, pp. 64–74, January–February, 1985.
Rights and permissions
About this article
Cite this article
Mirzoeva, T.M., Portenko, N.I. Limit theorems for functionals of irreversible random walks. Ukr Math J 37, 55–63 (1985). https://doi.org/10.1007/BF01056852
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01056852