Literature cited
J. Keilson and D. M. G. Wishart, “A central limit theorem for processes, defined on a finite Markov chain,” Proc. Cambridge Philos. Soc.,60, No. 3, 547–567 (1964).
M. Fukushima and M. Hitsuda, “On a class of Markov processes taking values on lines and the central limit theorem,” Nagoya Mathem. Journal,30, 47–56 (1967).
I. I. Ezkov and A. V. Skorokhod, “Markov processes homogeneous in the second component,” Teoriya Veroyatnostei i ee Primeneniya,14, No. 1 (1969).
É L. Presman, “Methods of factorization and the boundary problem for sums of random quantities defined on a Markov chain,” Izv. Akad. Nauk SSSR, Ser. Matem.,33, No. 4 (1969).
D. V. Gusak, “On continuous passage through fixed level with a homogeneous process with independent increments on a Markov chain,” Second Japan-USSR Symposium on Probability Theory, Vol. 1, pp. 12–21 (1972).
D. V. Gusak, “Extreme values of nondegenerate Wiener processes controlled by a finite Markov chain,” Teoriya Veroyatnostei i Matematicheskaya Statistika, No. 6 (1972).
B. A. Rogozin, “Distribution of certain functionals connected with boundary problems for processes with independent increments,” Teoriya Veroyatnostei i ee primeneniya, 11, No. 4 (1966).
J. Kemeni and J. Snell, Finite Markov Chains [in Russian], Nauka, Moscow (1970).
M. G. Krein and I. Ts. Gokhberg, “Systems of integral equations on the half-line with kernels depending on a variety of arguments,” UMN,13, No. 2 (1958).
D. V. Gusak, Canonical and Infinitesimal Factorization [in Russian], Dokl. Akad. Nauk URSR, Ser. A, No. 4 (1969).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 25, No. 2, pp. 170–178, March–April, 1973.
Rights and permissions
About this article
Cite this article
Gusak, D.V. A class of processes with independent increments on a finite Markov chain. Ukr Math J 25, 139–145 (1973). https://doi.org/10.1007/BF01096972
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01096972