Abstract
The transition probabilities we are interested in are defined for all real t ≥ 0 and satisfy the relations
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Uch. Zap. Moskov. Gos. Univ. Mat.148:4 (1951), 53-59.
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References
A.N. Kolmogorov, ‘On analytic methods in probability theory’, Uspekhi Mat. Nauk 5 (1938), 5–41.
W. Doeblin, ‘Sur l’équation matricielle A (t +s) = A (t) A(s), Bull. Sci. Math. 62 (1938), 21–32
J.L. Doob, ‘Topics in the theory of Markoff chains’, Trans. Amer. Math. Soc. 52 (1942), 37–64.
J.L. Doob, ‘Markoff chains — denumerable case’, Thins. Amer. Math. Soc. 58 (1945), 455–473.
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Shiryayev, A.N. (1992). On Differentiability of Transition Probabilities of Time-Homogeneous Markov Processes with A Countable Number of States. In: Shiryayev, A.N. (eds) Selected Works of A. N. Kolmogorov. Mathematics and Its Applications (Soviet Series), vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2260-3_39
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