Article PDF
References
Brown, J.R.: Approximation theorems for Markov operators. Pacific J. Math. 16, 13–23 (1966).
Doob, J.L.: Stochastic processes. New York: Wiley 1953.
—: A ratio operator limit theorem. Z. Wahrscheinlichkeitstheorie verw. Geb. 1, 288–294 (1963).
Dunford, N., Schwartz, J.T.: Linear operators, part I. New York: Interscience 1967.
Halmos, P.R., Neumann, J. von: Operator methods in classical mechanics. Ann. of Math. II. Ser. 43, 332–350 (1942).
Helms, L.L.: Mean convergence of martingales. Trans. Amer. math. Soc. 87, 439–446 (1958).
Kim, C.W.: Uniform approximation of doubly stochastic operators. Pacific J. Math. 26, 515–527 (1968).
Marcus, M., Minc, H.: A survey of matrix theory and matrix inequalities. Boston: Allyn and Bacon 1964.
Moy, S.-T.C: λ-continuous Markov chains. Trans. Amer. math. Soc. 117, 68–91 (1965).
Neveu, J.: Mathematical foundations of the calculus of probability. San Francisco: Holden-Day 1965.
Author information
Authors and Affiliations
Additional information
This work was supported in part by NSF Grant GP-5270 and in part by NRC Grant A-4844.
Rights and permissions
About this article
Cite this article
Kim, CW. Approximation theorems for Markov operators. Z. Wahrscheinlichkeitstheorie verw Gebiete 21, 207–214 (1972). https://doi.org/10.1007/BF00538394
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00538394