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Markov additive processes. I. (English) Zbl 0236.60047


MSC:

60J25 Continuous-time Markov processes on general state spaces
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[1] Blumenthal, R. M., Getoor, R. K.: Markov Processes and Potential Theory. New York: Academic Press 1968. · Zbl 0169.49204
[2] Çinlar, E.: Markov renewal theory. Advances appl. Probab. 1, 123-187 (1969). · Zbl 0212.49601
[3] Çinlar, E.: Markov Additive Processes II. Z. Wahrscheinlichkeitstheorie verw. Geb. 24, 95-121 (1972). · Zbl 0236.60048
[4] Doob, J. L.: Stochastic Processes. New York: Wiley 1953. · Zbl 0053.26802
[5] Ezhov, I. I., Skorohod, A. V.: Markov processes with homogeneous second component: I. Teor. Verojatn. Primen. 14, 1-13 (1969).
[6] Fukushima, M., Hitsuda, M.: On a class of Markov processes taking values on lines and the central limit theorem. Nagoya math. J. 30, 47-56 (1967). · Zbl 0178.20603
[7] Keilson, J., Wishart, D. M. G.: A central limit theorem for processes defined on a finite Markov chain. Proc. Cambridge Philos. Soc. 60, 547-567 (1964). · Zbl 0126.33504
[8] Keilson, J., Wishart, D. M. G.: Boundary problems for additive processes defined on a finite Markov chain. Proc. Cambridge philos. Soc. 61, 173-190 (1965). · Zbl 0138.40703
[9] Lévy, P.: Processus semi-markoviens. Proc. Int. Congr. Math. (Amsterdam) 3, 416-426 (1954).
[10] Miller, H. D.: A convexity property in the theory of random variables defined on a finite Markov chain. Ann. math. Statistics 32, 1260-1270 (1961). · Zbl 0108.15101
[11] Miller, H. D.: Absorbtion probabilities for sums of random variables defined on a finite Markov chain. Proc. Cambridge philos. Soc. 58, 286-298 (1962). · Zbl 0114.33703
[12] Neveu, J.: Une généralisation des processus à accroissements positifs indépendants. Abh. math. Sem. Univ. Hamburg 25, 36-61 (1961). · Zbl 0103.36303
[13] Pinsky, M.: Differential equations with a small parameter and the central limit theorem for functions defined on a finite Markov chain. Z. Wahrscheinlichkeitstheorie verw. Geb. 9, 101-111 (1968). · Zbl 0155.24203
[14] Pyke, R.: Markov renewal processes: definitions and preliminary properties. Ann. math. Statistics 32, 1231-1242(1961). · Zbl 0267.60089
[15] Pyke, R., Schaufele, R.: Limit theorems for Markov renewal processes. Ann. math. Statistics 35, 1746-1764 (1964). · Zbl 0134.34602
[16] Pyke, R., Schaufele, R.: The existence and uniqueness of stationary measures for Markov renewal processes. Ann. math. Statistics 37, 1439-1462 (1966). · Zbl 0154.42901
[17] Smith, W. L.: Regenerative stochastic processes. Proc. roy. Soc. London, Ser. A, 232, 6-31 (1955). · Zbl 0067.36301
[18] Volkov, I. S.: On probabilities for extreme values of sums of random variables defined on a homogeneous Markov chain with a finite number of states. Teor. Verojatn. Primen 5, 338-352 (1960). · Zbl 0096.34005
[19] Walsh, J. B.: The perfection of multiplicative functionals. Lecture Notes Math. 258: Séminaire de ProbabilitésVI, 233-242 (1972). · Zbl 0241.60061
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