Brownian Motion—Wiener Process
Canadian mathematical bulletin, Tome 22 (1979) no. 3, pp. 257-279

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Bachelier (1900), Einstein (1905) and Smoluchowski (1915) provided a theory of the peculiar erratic motion of small particles suspended in a liquid, first described in 1826 by the English botanist Brown. In a series of papers beginning in 1920 Wiener undertook a mathematical analysis of Brownian motion.
Csörgő, Miklós. Brownian Motion—Wiener Process. Canadian mathematical bulletin, Tome 22 (1979) no. 3, pp. 257-279. doi: 10.4153/CMB-1979-033-1
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[1] 1. Bachelier, L., Théorie de la spéculation, Ann. Sci. Ecole Norm. Sup. 17 (1900), 21-86. Google Scholar

[2] 2. Book, S. A. and Shore, T. R., On large intervals in the Csörgő-Révész theorem on increments of a Wiener process, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 46 (1978), 1-11. Google Scholar

[3] 3. Chan, A. H. C., Csörgő, M. and Révész, P., Strassen type limit points for moving averages of a Wiener process, Can. J. Statist. 6 (1978), 57-75. Google Scholar

[4] 4. Chung, K. L., On the maximum partial sums of sequences of independent random variables, Trans. Amer. Math. Soc. 64 (1948), 205-233. Google Scholar

[5] 5. Chung, K. L., A Course in Probability Theory, Harcourt, Brace & World, New York, 1968. Google Scholar

[6] 6. Csâki, E. and Révész, P., How big must be the increments of a Wiener process? (1979), to appear. Google Scholar

[7] 7. Csörgő, M. and Révész, P., How big are the increments of a Wiener process? Ann. Probability, (1979a), to appear. Google Scholar

[8] 8. Csörgő, M. and Révész, P., How small are the increments of a Wiener process? Stochastic Processes and their Applications, 8 (1979b), 119-129. Google Scholar

[9] 9. Csörgő, M. and Révész, P., Strong Approximations in Probability and Statistics, (1979c), Book manuscript in progress. Google Scholar

[10] 10. Deo, C. M., A note on increments of a Wiener process, Technical Report, University of Ottawa, 1977. Google Scholar

[11] 11. Doob, J. L., Stochastic Processes, John Wiley, New York, 1953. Google Scholar

[12] 12. Einstein, A., On the movement of small particles suspended in a stationary liquid demanded by the molecular-kinetic theory of heat, Ann. Physik, 17 (1905), 549-560. Google Scholar

[13] 13. Erdôs, P. and Rényi, A., On a new law of large numbers, J. Analyse Math., 13 (1970), 103-111. Google Scholar

[14] 14. Feller, W., An Introduction to Probability Theory and its Applications I, John Wiley, New York, 1968. Google Scholar

[15] 15. Hirsh, W. M., A strong law for the maximum cumulative sum of independent random variables, Comm. Pure Appl. Math., 18 (1965), 109-127. Google Scholar

[16] 16. Itô, K., Stochastic integral, Proc. Imperial Acad., Tokyo, 20 (1944), 519-524. Google Scholar

[17] 17. Itô, K. and Nisio, M., On the oscillation functions of Gaussian processes, Math. Scand., 22 (1968), 209-223. Google Scholar

[18] 18. Kolmogorov, A. N., Grundbegriffe der Wahrscheinlichkeitsrechnung, Springer, Berlin, 1933. Google Scholar

[19] 19. Levy, P., Théorie de VAddition des Variables Aléatoires, Gauthier-Villars, Paris, 1937. Google Scholar

[20] 20. Levy, P., Processus Stochastiques et Mouvement Brownien, Gauthier-Villars, Paris, 1948. Google Scholar

[21] 21. McKean, H. P. Jr. Stochastic Integrals, Academic Press, New York, 1969. Google Scholar

[22] 22. Paley, R. E. A. C. and Wiener, N., Fourier Transforms in the complex domain, Amer. Math. Soc. Colloq. Publ., Vol. 19, Amer. Math. Soc, Providence, R.I., 1934. Google Scholar

[23] 23. Paley, R. E. A. C., Wiener, N. and Zygmund, A., Note on random functions, Math. Z., 37 (1959), 647-668. Google Scholar

[24] 24. Smoluchowski, M., Über Brownsche Molekular-bewegung, Ann. Phys., 48 (1915), 110-120. Google Scholar

[25] 25. Strassen, V., An invariance principle for the law of interated logarithm, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 3, (1964), 211-226. Google Scholar

[26] 26. Wiener, N., The mean of a functional of arbitrary elements, Ann. of Math., 22 (1920), 66-72. Google Scholar

[27] 27. Wiener, N., Differential space, J. Math and Phys., 2 (1923), 132-174. Google Scholar

[28] 28. Wiener, N., Generalized harmonic analysis, Acta Math. 55 (1930), 117-258. Google Scholar

[29] 29. Wiener, N., I am a mathematician. The later life of a prodigy, Doubleday, New York, 1956. Google Scholar

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