Frontiers of Mathematics in China >
Mean and variance of first passage time of non-homogeneous random walk
Received date: 09 Sep 2010
Accepted date: 20 Dec 2011
Published date: 01 Jun 2012
Copyright
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
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
1 |
Alili S. Asymptotic behavior for random walks in random environments. J Appl Prob, 1999, 36: 334-349
|
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
|
/
〈 | 〉 |