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. Statistics**23**(1952), 193–212. MR**0050238****[2]**Monroe D. Donsker,*An invariance principle for certain probability limit theorems*, Mem. Amer. Math. Soc.,**No. 6**(1951), 12. MR**0040613****[3]**Monroe D. Donsker,*Justification and extension of Doob’s heuristic approach to the Komogorov-Smirnov theorems*, Ann. Math. Statistics**23**(1952), 277–281. MR**0047288****[4]**J. L. Doob,*Heuristic approach to the Kolmogorov-Smirnov theorems*, Ann. Math. Statistics**20**(1949), 393–403. MR**0030732****[5]**J. L. Doob,*Stochastic processes*, John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. MR**0058896****[6]**B. V. Gnedenko and A. N. Kolmogorov,*Limit distributions for sums of independent random variables*, Addison-Wesley Publishing Company, Inc., Cambridge, Mass., 1954. Translated and annotated by K. L. Chung. With an Appendix by J. L. Doob. MR**0062975****[7]**P. Erdös and M. Kac,*On certain limit theorems of the theory of probability*, Bull. Amer. Math. Soc.**52**(1946), 292–302. MR**0015705**, https://doi.org/10.1090/S0002-9904-1946-08560-2**[8]**P. Erdös and M. Kac,*On the number of positive sums of independent random variables*, Bull. Amer. Math. Soc.**53**(1947), 1011–1020. MR**0023011**, https://doi.org/10.1090/S0002-9904-1947-08928-X**[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, 1950, University of California Press, Berkeley and Los Angeles, 1951, pp. 189–215. MR**0045333**

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

Article copyright:
© Copyright 1957
American Mathematical Society