scholarly journals A PDE hierarchy for directed polymers in random environments

Nonlinearity ◽  
2021 ◽  
Vol 34 (10) ◽  
pp. 7335-7370
Author(s):  
Yu Gu ◽  
Christopher Henderson
Keyword(s):  
Directed Polymers ◽  
Random Environments

scholarly journals A remark on diffusion of directed polymers in random environments

1996 ◽  
Vol 85 (1-2) ◽  
pp. 277-289 ◽  
Author(s):  
Renming Song ◽  
Xian Yin Zhou
Keyword(s):  
Directed Polymers ◽  
Random Environments

On calculating extinction probabilities for branching processes in random environments

1969 ◽  
Vol 6 (03) ◽  
pp. 478-492 ◽  
Author(s):  
William E. Wilkinson
Keyword(s):  
Generating Functions ◽  
Infinite Sequence ◽  
Branching Processes ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Random Environments ◽  
Real Numbers ◽  
Discrete Time Markov Chain ◽  
Extinction Probabilities ◽  
Image Position

Consider a discrete time Markov chain {Zn } whose state space is the non-negative integers and whose transition probability matrix ║Pij ║ possesses the representation where {Pr }, r = 1,2,…, is a finite or denumerably infinite sequence of non-negative real numbers satisfying , and , is a corresponding sequence of probability generating functions. It is assumed that Z 0 = k, a finite positive integer.

scholarly journals A comparison of random walks in dependent random environments

2016 ◽  
Vol 48 (1) ◽  
pp. 199-214
Author(s):  
Werner R. W. Scheinhardt ◽  
Dirk P. Kroese
Keyword(s):  
Random Walks ◽  
Random Environment ◽  
Moving Average ◽  
Random Environments ◽  
Dependency Structure ◽  
Interesting Behavior

Abstract We provide exact computations for the drift of random walks in dependent random environments, including k-dependent and moving average environments. We show how the drift can be characterized and evaluated using Perron–Frobenius theory. Comparing random walks in various dependent environments, we demonstrate that their drifts can exhibit interesting behavior that depends significantly on the dependency structure of the random environment.

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