Literature Cited
R. V. Boiko, “On the distribution of the number of incidences in a segment in a Bernoulli random walk scheme,” Dokl. Akad. Nauk URSR, Ser. A, No. 12, 1059–1063 (1970).
W. Feller, Introduction to Probability Theory and Its Application [Russian translation], Vol. 1, Mir, Moscow (1967).
É. L. Presman, “Factorization methods and boundary value problem for sums of random variables given on Markov chains,” Izv. Akad. Nauk SSSR, Ser. Mat.,33, No. 4, 861–900 (1969).
A. A. Borovkov, “Limit theorems on the distributions of the maximum of sums of bounded lattice random variables I, II,” Teor. Veroyatn. i Ee Primeneniya,5, No. 2, 137–171; No. 4, 377–392 (1960).
A. A. Borovkov, “New limit theorems in boundary value problems for sums of independent components,” Sib. Matem. Zh.,3, No. 5, 645–694 (1962).
I. S. Volkov, “On the distribution of sums of random variables given on a homogeneous Markov chain with a finite number of states,” Teor. Veroyatn. i Ee Primeneniya,3, No. 4, 413–429 (1958).
H. D. Miller, “A convexity property in the theory of random variables defined on a finite Markov chain,” Ann. Math. Statistics,32, No. 4, 1260–1270 (1961).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 14, No. 4, pp. 816–826, July–August, 1973.
Rights and permissions
About this article
Cite this article
Semenov, A.T. Asymptotic expansions for the distribution of the number of incidences in symmetric Bernoulli random walk segments. Sib Math J 14, 565–572 (1973). https://doi.org/10.1007/BF00967551
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00967551