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Perturbed semigroup limit theorems with applications to discontinuous random evolutions. (English) Zbl 0263.47034


MSC:

47D03 Groups and semigroups of linear operators
60F05 Central limit and other weak theorems
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[1] R. M. Blumenthal and R. K. Getoor, Markov processes and potential theory, Pure and Applied Mathematics, Vol. 29, Academic Press, New York-London, 1968. · Zbl 0169.49204
[2] E. Çinlar and M. Pinsky, A stochastic integral in storage theory, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 17 (1971), 227 – 240. · Zbl 0195.47503 · doi:10.1007/BF00536759
[3] R. Cogburn and R. Hersh, Two limit theorems for random differential equations, Indiana Univ. Math. J. 22 (1972/73), 1067 – 1089. · Zbl 0246.60048 · doi:10.1512/iumj.1973.22.22090
[4] J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. · Zbl 0053.26802
[5] Марковские процессы, Государств. Издат. Физ.-Мат. Лит., Мосцощ, 1963 (Руссиан). · Zbl 0132.37701
[6] Richard Griego and Reuben Hersh, Theory of random evolutions with applications to partial differential equations, Trans. Amer. Math. Soc. 156 (1971), 405 – 418. · Zbl 0223.35082
[7] R. Hersh and G. Papanicolaou, Non-commuting random evolutions, and an operator-valued Feynman-Kac formula, Comm. Pure Appl. Math. 25 (1972), 337 – 367. · Zbl 0232.60054 · doi:10.1002/cpa.3160250307
[8] Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. · Zbl 0078.10004
[9] A. M. Il\(^{\prime}\)in and R. Z. Has\(^{\prime}\)minskiĭ, On the equations of Brownian motion, Teor. Verojatnost. i Primenen. 9 (1964), 466 – 491 (Russian, with English summary).
[10] R. P. Kertz, Limit theorems for discontinuous random evolutions, Ph. D. Dissertation, Northwestern University, Evanston, Ill., 1972.
[11] Robert P. Kertz, Limit theorems for discontinuous random evolutions with applications to initial value problems and to Markov processes on \? lines, Ann. Probability 2 (1974), 1046 – 1064. · Zbl 0323.60064
[12] Thomas G. Kurtz, Extensions of Trotter’s operator semigroup approximation theorems, J. Functional Analysis 3 (1969), 354 – 375. · Zbl 0174.18401
[13] Thomas G. Kurtz, A general theorem on the convergence of operator semigroups, Trans. Amer. Math. Soc. 148 (1970), 23 – 32. · Zbl 0194.44103
[14] Thomas G. Kurtz, A limit theorem for perturbed operator semigroups with applications to random evolutions, J. Functional Analysis 12 (1973), 55 – 67. · Zbl 0246.47053
[15] Mark A. Pinsky, Multiplicative operator functionals of a Markov process, Bull. Amer. Math. Soc. 77 (1971), 377 – 380. · Zbl 0255.60053
[16] Mark A. Pinsky, Multiplicative operator functionals and their asymptotic properties, Advances in probability and related topics, Vol. 3, Dekker, New York, 1974, pp. 1 – 100. · Zbl 0342.60012
[17] A. Sommerfeld, Mechanics. Lectures on theoretical physics. Vol. 1, Translated from the 4th German edition; Academic Press, New York, 1952. MR 14, 419. · Zbl 0048.41806
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