On the convergence of sequences of stochastic processes

Author:
Ernest G. Kimme

Journal:
Trans. Amer. Math. Soc. **84** (1957), 208-229

MSC:
Primary 60.0X

DOI:
https://doi.org/10.1090/S0002-9947-1957-0083843-5

MathSciNet review:
0083843

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References | Similar Articles | Additional Information

**[1]**T. W. Anderson and D. A. Darling,*Asymptotic theory of certain goodness of fit criteria based on stochastic processes*, Ann. Math. Statist, vol. 23 (1952) pp. 193-212. MR**0050238 (14:298h)****[2]**M. D. Donsker,*An invariance principle for certain probability limit theorems*, Memoirs of the American Mathematical Society, no. 6, 1951, pp. 1-12. MR**0040613 (12:723a)****[3]**-,*Justification and extension of Doob's heuristic approach to the Kolmogorov-Smirnov theorems*, Ann. Math. Statist. vol. 23 (1952) pp. 277-281. MR**0047288 (13:853n)****[4]**J. Doob,*Heuristic approach to the Kolmogorov-Smirnov theorems*, Ann. Math. Statist. vol. 20 (1949) pp. 393-403. MR**0030732 (11:43a)****[5]**-,*Stochastic processes*, Wiley, 1953. MR**0058896 (15:445b)****[6]**B. V. Gnedenko and A. N. Kolmogorov,*Limit distributions for sums of independent random variables*, Addison-Wesley, 1954. MR**0062975 (16:52d)****[7]**M. Kac and P. Erdös,*On certain limit theorems of the theory of probability*, Bull. Amer. Math. Soc. vol. 52 (1946) pp. 292-302. MR**0015705 (7:459b)****[8]**-,*On the number of positive sums of independent random variables*, Bull. Amer. Math. Soc. vol. 53 (1947) pp. 1011-1020. MR**0023011 (9:292g)****[9]**M. Kac,*On some connections between probability theory and differential and integral equations*, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley and Los Angeles, 1950, pp. 189-216. MR**0045333 (13:568b)**

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DOI:
https://doi.org/10.1090/S0002-9947-1957-0083843-5

Article copyright:
© Copyright 1957
American Mathematical Society