• [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 (14,298h)
• [2] Leo Breiman, Probability, Addison-Wesley Publishing Company, Reading, Mass., 1968. MR 0229267 (37 #4841)
• [3] R. Courant and D. Hilbert, Methods of mathematical physics, Vol. 1, Interscience, New York, 1963.
• [4] 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 (13,853n)
• [5] J. L. Doob, Heuristic approach to the Kolmogorov-Smirnov theorems, Ann. Math. Statistics 20 (1949), 393–403. MR 0030732 (11,43a)
• [6] B. V. Gnedenko, V. S. Koroluk, and A. V. Skorohod, Asymptotic expansions in probability theory, Proc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. II, Univ. California Press, Berkeley, Calif., 1961, pp. 153–170. MR 0133845 (24 #A3669)
• [7] Samuel Karlin, A first course in stochastic processes, Academic Press, New York, 1966. MR 0208657 (34 #8466)
• [8] A. N. Kolmogorov, Sulla determinazione emperica delle leggi di probabilita, Giorn. Ist. Ital. Attuari 4 (1933), 1-11.
• [9] K. R. Parthasarathy, Probability measures on metric spaces, Probability and Mathematical Statistics, No. 3, Academic Press Inc., New York, 1967. MR 0226684 (37 #2271)
• [10] Yu. V. Prochorov, Convergence of random processes and limit theorems in probability, Theor. Probability Appl. 1 (1956), 157-214.
• [11] Walter A. Rosenkrantz, On rates of convergence for the invariance principle, Trans. Amer. Math. Soc. 129 (1967), 542–552. MR 0215347 (35 #6188), http://dx.doi.org/10.1090/S0002-9947-1967-0215347-7
• [12] A. V. Skorokhod, Studies in the theory of random processes, Translated from the Russian by Scripta Technica, Inc, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. MR 0185620 (32 #3082b)

Bibliography

[1]

D. A. Darling and T. W. Anderson, Asymptotic theory of certain ``goodness of fit'' criteria based on stochastic processes, Ann. Math. Statist. 23 (1952), 193-212. MR 0050238 (14:298h)

[2]

L. Breiman, Probability, Addison-Wesley, Reading, Mass., 1968. MR 0229267 (37:4841)

[3]

R. Courant and D. Hilbert, Methods of mathematical physics, Vol. 1, Interscience, New York, 1963.

[4]

M. Donsker, Justification and extension of Doob's heuristic approach to the Kolmogorov-Smirnov theorems, Ann. Math. Statist. 23 (1952), 277-281. MR 0047288 (13:853n)

[5]

J. L. Doob, Heuristic approach to the Kolmogorov-Smirnov theorems, Ann. Math. Statist. 20 (1949), 393-403. MR 0030732 (11:43a)

[6]

B. V. Gnedenko, V. S. Korolyuk and A. V. Skorokhod, Asymptotic expansions in probability theory, Proc. Fourth Berkeley Sympos. Math. Stat. and Prob. (1960), Vol. II, Univ. California Press, Berkeley, Calif., 1961, pp. 153-170. MR 0133845 (24:A3669)

[7]

S. Karlin, A first course in stochastic processes, Academic Press, New York, 1966. MR 0208657 (34:8466)

[8]

A. N. Kolmogorov, Sulla determinazione emperica delle leggi di probabilita, Giorn. Ist. Ital. Attuari 4 (1933), 1-11.

[9]

K. R. Parthasarathy, Probability measures on metric spaces, Academic Press, New York, 1967. MR 0226684 (37:2271)

[10]

Yu. V. Prochorov, Convergence of random processes and limit theorems in probability, Theor. Probability Appl. 1 (1956), 157-214.

[11]

W. A. Rosenkrantz, On rates of convergence for the invariance principle, Trans. Amer. Math. Soc. 129 (1967), 542-552. MR 0215347 (35:6188)

[12]

A. V. Skorokhod, Studies in the theory of random processes, Addison-Wesley, Reading, Mass., 1965. MR 0185620 (32:3082b)