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 Electronic Journal of Probability > Vol. 11 (2006) > Paper 44 open journal systems 


Infinitely divisible random probability distributions with an application to a random motion in a random environment

Tokuzo Shiga, Tokyo Institute of Technology
Hiroshi Tanaka, Keio University


Abstract
The infinite divisibility of probability distributions on the space $P (R )$ of probability distributions on $R$ is defined and related fundamental results such as the L'{e}vy-Khintchin formula, representation of It^{o} type of infinitely divisible RPD, stable RPD and L'{e}vy processes on $P (R )$ are obtained. As an application we investigate limiting behaviors of a simple model of a particle motion in a random environment


Full text: PDF

Pages: 1144-1183

Published on: December 7, 2006
Bibliography
  1. Brox, Th. A one-dimensional diffusion process in a Wiener medium. Ann. Probab. 14 (1986), Springer, New York, 1995. Math. Review 88f:60132
  2. Chow, Yuan Shih; Teicher, Henry. Probability theory. Independence, interchangeability, martingales , Springer, New York-Heidelberg, 1978. Math. Review 80a:60004
  3. Feller, William An introduction to probability theory and its applications. Vol. II , John Wiley & Sons, Inc., New York-London-Sydney 1966. Math. Review 35 #1048
  4. Hu, Yueyun; Shi, Zhan; Yor, Marc. Rates of convergence of diffusions with drifted Brownian potentials. Ann. Probab. 351 (1999), 3915--3934. Math. Review 99m:60119
  5. Ito, Kiyosi. Stochastic processes. Lectures given at Aarhus University. Reprint of the 1969 original. Edited and with a foreword by Ole E. Barndorff-Nielsen and Ken-iti Sato., Springer, Berlin, 2004. Math. Review 2005e:60002
  6. Kasahara, Yuji; Watanabe, Shinzo. Limit theorems for point processes and their functionals. J. Math. Soc. Japan 38 (1986), 543-574. Math. Review 88b:60058
  7. Kawazu, Kiyoshi; Tanaka, Hiroshi. A diffusion process in a Brownian environment with drift. J. Math. Soc. Japan 49 (1997), no. 2, 189-211. Math. Review 99c:60170
  8. Kesten, H.; Kozlov, M. V.; Spitzer, F. A limit law for random walk in a random environment. Compositio Math. 30 (1975), 145-168. Math. Review 52 #1895
  9. Sato, Ken-iti. Levy processes and infinitely divisible distributions. Translated from the 1990 Japanese original. Revised by the author. , Cambridge University Press, Cambridge, 1999. Math. Review 2003b:60064
  10. Solomon, Fred. Random walks in a random environment. Ann. Probability 3 (1975), 1-31. Math. Review 50 #14943
  11. Sinaui, Ya. G. The limit behavior of a one-dimensional random walk in a random environment. (Russian) Teor. Veroyatnost. i Primenen. 27 (1982), 247--258. Math. Review 83k:60078
  12. Tanaka, Hiroshi. Environment-wise central limit theorem for a diffusion in a Brownian environment with large drift. Ito's stochastic calculus and probability theory, 373-384 . Springer, Tokyo, 1996. Math. Review 98k:60135
  13. Tanaka, Hiroshi. Limit theorems for a Brownian motion with drift in a white noise environment. Chaos Solitons Fractals 8 (1997),1807-1816. Math. Review 99a:60085
















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Electronic Journal of Probability. ISSN: 1083-6489