• [I] Warren Ambrose, On measurable stochastic processes, Trans. Amer. Math. Soc. 47 (1940), 66–79. MR 0000918, https://doi.org/10.1090/S0002-9947-1940-0000918-4
• [II] D. A. Darling and A. J. F. Siegert, The first passage problem for a continuous Markov process, Ann. Math. Statistics 24 (1953), 624–639. MR 0058908
• [III] W. Doblin, Sur l'équation de Kolmogoroff, C. R. Acad. Sci. Paris vol. 207 (1938) pp. 705-707.
• [IV] J. L. Doob, Stochastic processes depending on a continuous parameter, Trans. Amer. Math. Soc. 42 (1937), no. 1, 107–140. MR 1501916, https://doi.org/10.1090/S0002-9947-1937-1501916-1
• [V] -, Stochastic processes, New York, 1953.
• [VI] J. L. Doob, Semimartingales and subharmonic functions, Trans. Amer. Math. Soc. 77 (1954), 86–121. MR 0064347, https://doi.org/10.1090/S0002-9947-1954-0064347-X
• [VII] William Feller, Diffusion processes in one dimension, Trans. Amer. Math. Soc. 77 (1954), 1–31. MR 0063607, https://doi.org/10.1090/S0002-9947-1954-0063607-6
• [VIII] William Feller, The general diffusion operator and positivity preserving semi-groups in one dimension, Ann. of Math. (2) 60 (1954), 417–436. MR 0065809, https://doi.org/10.2307/1969842
• [IX] William Feller, On second order differential operators, Ann. of Math. (2) 61 (1955), 90–105. MR 0068082, https://doi.org/10.2307/1969621
• [X] Robert Fortet, Les fonctions aléatoires du type de Markoff associées à certaines équations linéaires aux dérivées partielles du type parabolique, J. Math. Pures Appl. (9) 22 (1943), 177–243 (French). MR 0012392
• [XI] D. C. Gillespie and W. A. Hurwitz, On sequences of continuous functions having continuous limits, Trans. Amer. Math. Soc. 32 (1930), no. 3, 527–543. MR 1501551, https://doi.org/10.1090/S0002-9947-1930-1501551-9
• [XII] Einar Hille, Functional Analysis and Semi-Groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, New York, 1948. MR 0025077
• [XIII] G. A. Hunt, Some theorems concerning Brownian motion, Trans. Amer. Math. Soc. 81 (1956), 294–319. MR 0079377, https://doi.org/10.1090/S0002-9947-1956-0079377-3
• [XIV] M. Kac, On some connections between probability theory and differential and integral equations, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley and Los Angeles, 1951, pp. 189–215. MR 0045333
• [XV] J. R. Kinney, Continuity properties of sample functions of Markov processes, Trans. Amer. Math. Soc. 74 (1953), 280–302. MR 0053428, https://doi.org/10.1090/S0002-9947-1953-0053428-1
• [XVI] A. Kolmogorov, Grundbegriffe der Wahrscheinlichkeitsrechnung, Ergebnisse der Math. vol. 2, Berlin, 1933.
• [XVII] Paul Lévy, Systèmes markoviens et stationnaires. Cas dénombrable, Ann. Sci. École Norm. Sup. (3) 68 (1951), 327–381 (French). MR 0047961
• [XVIII] E. B. Dynkin, Criteria of continuity and of absence of discontinuities of the second kind for trajectories of a Markov random process, Izvestiya Akad. Nauk. SSSR. Ser. Mat. 16 (1952), 563–572 (Russian). MR 0052055
• [XIX] E. B. Dynkin, Infinitesimal operators of Markov random processes, Dokl. Akad. Nauk SSSR (N.S.) 105 (1955), 206–209 (Russian). MR 0076221
• [XX] -, Continuous stationary Markov processes, Doklady Akademii Nauk SSSR. vol. 105 (1955) pp. 405-408.

Bibliography

[I]

W. Ambrose, On measurable stochastic processes, Trans. Amer. Math. Soc. vol. 47 (1940) pp. 66-79. MR 0000918 (1:149h)

[II]

D. A. Darling and A. J. F. Siegert, The first passage problem for a continuous Markoff process, Ann. Math. Statist, vol. 24 (1953) pp. 624-639. MR 0058908 (15:449f)

[III]

W. Doblin, Sur l'équation de Kolmogoroff, C. R. Acad. Sci. Paris vol. 207 (1938) pp. 705-707.

[IV]

J. L. Doob, Stochastic processes depending on a continuous parameter, Trans. Amer. Math. Soc. vol. 42 (1937) pp. 107-140. MR 1501916

[V]

-, Stochastic processes, New York, 1953.

[VI]

-, Semimartingales and subharmonic functions, Trans. Amer. Math. Soc. vol. 77 (1954) pp. 86-121. MR 0064347 (16:269a)

[VII]

W. Feller, Diffusion processes in one dimension, Trans. Amer. Math. Soc. vol. 77 (1954) pp. 1-31. MR 0063607 (16:150d)

[VIII]

-, The general diffusion operator and positivity preserving semi-groups in one dimension, Ann. of Math. vol. 60 (1954) pp. 417-436. MR 0065809 (16:488d)

[IX]

-, On second order differential operators, Ann. of Math. vol. 61 (1955) pp. 90-105. MR 0068082 (16:824g)

[X]

R. Fortet, Les fonctions aléatoires du type de Markoff associées à certaines équations linéaires aux dérivées partielles du type paraboliques, J. Math. Pures Appl. vol. 22 (1943) pp. 177-243. MR 0012392 (7:19h)

[XI]

D. C. Gillespie and W. A. Hurwitz, On sequences of continuous functions having continuous limits, Trans. Amer. Math. Soc. vol. 32 (1930) pp. 527-543. MR 1501551

[XII]

E. Hille, Semi-groups and functional analysis, American Mathematical Society Colloquium Publications 31, New York, 1948. MR 0025077 (9:594b)

[XIII]

G. A. Hunt, Some theorems concerning Brownian motion, Trans. Amer. Math. Soc. vol. 81 (1956) pp. 294-319. MR 0079377 (18:77a)

[XIV]

M. Kac, On some connections between probability theory and differential and integral equations, Proc. Second Berkeley Symposium on Mathematical Statistics and Probability, 1951, pp. 189-215. MR 0045333 (13:568b)

[XV]

J. R. Kinney, Continuity properties of sample functions of Markov processes, Trans. Amer. Math. Soc. vol. 74 (1953) pp. 280-302. MR 0053428 (14:772b)

[XVI]

A. Kolmogorov, Grundbegriffe der Wahrscheinlichkeitsrechnung, Ergebnisse der Math. vol. 2, Berlin, 1933.

[XVII]

P. Lévy, Systèmes markoviens et stationnaires, Ann. École Norm. (3) vol. 68 (1951) pp. 327-381. MR 0047961 (13:959c)

[XVIII]

E. B. Dynkin, Criteria of continuity for trajectories of a Markov random process, Izvestiya Akademii Nauk SSSR. Seriya Matematičeskaya vol. 16 (1952) pp. 563-572. MR 0052055 (14:567e)

[XIX]

-, Infinitesimal operators of Markov processes, Doklady Akademii Nauk SSSR. vol. 105 (1955) pp. 206-209. MR 0076221 (17:866d)

[XX]

-, Continuous stationary Markov processes, Doklady Akademii Nauk SSSR. vol. 105 (1955) pp. 405-408.