Proof of the law of iterated logarithm through diffusion equation

  • Minoru Motoo


Brownian Motion Diffusion Process Diffusion Equation Iterate Logarithm Infinitesimal Generator 


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    D. Ray: Stationary Markov process with continuous paths.Trans. of Amer. Math. Soc., vol. 82 (1956).Google Scholar
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    A. Dvoretzky and P. Erdös: Some problem on random walk in space.Proceedings of the 2nd Berkeley Symposium (1951).Google Scholar
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    F. Spitzer: Some theorems concerning 2-dimensional Brownian motion.Trans. of Amer. Math. Soc. vol. 87 (1958).Google Scholar
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    P. Lévy:Processus stochastique et mouvement brownien. Paris, 1948.Google Scholar
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    E. B. Dinkin: Infinitesimal operators of Markov processes.Theory of probability and its application, vol. 1, no. 1Google Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1959

Authors and Affiliations

  • Minoru Motoo
    • 1
  1. 1.The Institute of Statistical MathematicsJapan

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