Moment Generating Functions for Local Times of Symmetric Markov Processes and Random Walks

1992 ◽  
pp. 364-376 ◽  
Author(s):  
Michael B. Marcus ◽  
Jay Rosen
Keyword(s):  
Random Walks ◽  
Markov Processes ◽  
Generating Functions ◽  
Local Times ◽  
Moment Generating Functions ◽  
Symmetric Markov Processes

Wald's equations, first passage times and moments of ladder variables in Markov random walks

1998 ◽  
Vol 35 (3) ◽  
pp. 566-580 ◽  
Author(s):  
Cheng Der Fuh ◽  
Tze Leung Lai
Keyword(s):  
Random Walks ◽  
Asymptotic Expansions ◽  
Generating Functions ◽  
First Passage Times ◽  
First Passage ◽  
New Approach ◽  
Markov Random ◽  
Moment Generating Functions ◽  
Passage Times

Previous work in extending Wald's equations to Markov random walks involves finiteness of moment generating functions and uniform recurrence assumptions. By using a new approach, we can remove these assumptions. The results are applied to establish finiteness of moments of ladder variables and to derive asymptotic expansions for expected first passage times of Markov random walks. Wiener–Hopf factorizations for Markov random walks are also applied to analyse ladder variables and related first passage problems.

Wald's equations, first passage times and moments of ladder variables in Markov random walks

1998 ◽  
Vol 35 (03) ◽  
pp. 566-580 ◽  
Author(s):  
Cheng Der Fuh ◽  
Tze Leung Lai
Keyword(s):  
Random Walks ◽  
Asymptotic Expansions ◽  
Generating Functions ◽  
First Passage Times ◽  
First Passage ◽  
New Approach ◽  
Markov Random ◽  
Moment Generating Functions ◽  
Passage Times

Previous work in extending Wald's equations to Markov random walks involves finiteness of moment generating functions and uniform recurrence assumptions. By using a new approach, we can remove these assumptions. The results are applied to establish finiteness of moments of ladder variables and to derive asymptotic expansions for expected first passage times of Markov random walks. Wiener–Hopf factorizations for Markov random walks are also applied to analyse ladder variables and related first passage problems.

Coherent random walks arising in some genetical models

1976 ◽  
Vol 351 (1664) ◽  
pp. 19-31 ◽  
Keyword(s):  
Population Genetics ◽  
Random Walks ◽  
Markov Processes ◽  
Stochastic Models ◽  
Equilibrium Distribution ◽  
Large Sample ◽  
Random Variation

Certain stochastic models used in population genetics have the form of Markov processes in which a group of N points moves randomly on a line, and in which an equilibrium distribution exists for the relative configura­tion of the group. The properties of this equilibrium are studied, with particular reference to a certain limiting situation as N becomes large. In this limit the group of points is distributed like a large sample from a distribution which is itself subject to random variation.

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