The correlated random walk in continuous time with barriers
作者:
Asha Seth Kapadia,
期刊:
Canadian Journal of Statistics
(WILEY Available online 1975)
卷期:
Volume 3,
issue 1
页码: 45-56
ISSN:0319-5724
年代: 1975
DOI:10.2307/3315098
出版商: Wiley‐Blackwell
关键词: Random walk, correlated, barrier, absorbing, reflecting, transitions, unrestricted, stationary
数据来源: WILEY
摘要:
AbstractIn this paper correlation has been introduced between two successive transitions in the model investigated by Moyal and Heathcote (1959). The transition rate has been taken to be constant and for simplicity of mathematical expressions the time scale has been so chosen that this rate is unity. For the unrestricted walk we find that the mean position of the particle at time t is that position for which the probability of the particle arriving at some earlier instant from the left is 1/2. With both the barriers either absorbing or reflecting, we have obtained the Laplace Transform of the distributions, but because of the complicated nature of the mathematical expressions involved we are able to find only the asymptotic distributions. For the reflecting barrier case, we find that the process tends to a stationary distribution and that the expected position is eventually the middle point between the barriers.
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