Frontiers of Mathematics in China >

2012 , Vol. 7 >Issue 3: 551 - 559

DOI: https://doi.org/10.1007/s11464-012-0175-8

RESEARCH ARTICLE

Mean and variance of first passage time of non-homogeneous random walk

  • Huaming WANG
Expand
  • Business College, Beijing Union University, Beijing 100025, China

Received date: 09 Sep 2010

Accepted date: 20 Dec 2011

Published date: 01 Jun 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
Fold

Abstract

The prime concern of this paper is the first passage time of a nonhomogeneous random walk, which is nearest neighbor but able to stay at its position. It is revealed that the branching structure of the walk corresponds to a 2-type non-homogeneous branching process and the first passage time of the walk can be expressed by that branching process. Therefore, one can calculate the mean and variance of the first passage time, though its exact distribution is unknown.

Key words： Random walk; 2-type branching process; first passage time; variance

Cite this article

Huaming WANG . Mean and variance of first passage time of non-homogeneous random walk[J]. Frontiers of Mathematics in China, 2012 , 7(3) : 551 -559 . DOI: 10.1007/s11464-012-0175-8

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Alili S. Asymptotic behavior for random walks in random environments. J Appl Prob, 1999, 36: 334-349

DOI

2
Strook D W. An Introduction to Markov Processes. Berlin: Springer-Verlag, 2005

3
Zeitouni O. Random walks in random environment. In: PicardJ, ed. Lectures on Probability Theory and Statistics. Lecture Notes in Mathematics, Vol 1837. Berlin: Springer-Verlag, 2004, 189-312

Options
Outlines

/

〈 〉