Transition probability matrices for correlated random walks

1980 ◽  
Vol 17 (01) ◽  
pp. 253-258 ◽  
Author(s):  
R. B. Nain ◽  
Kanwar Sen
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Difference Equations ◽  
Generating Functions ◽  
Transition Probability ◽  
Correlated Random Walk ◽  
One Dimensional ◽  
Correlated Random Walks ◽  
Transition Probability Matrices ◽  
Probability Matrices

For correlated random walks a method of transition probability matrices as an alternative to the much-used methods of probability generating functions and difference equations has been investigated in this paper. To illustrate the use of transition probability matrices for computing the various probabilities for correlated random walks, the transition probability matrices for restricted/unrestricted one-dimensional correlated random walk have been defined and used to obtain some of the probabilities.

Transition probability matrices for correlated random walks

1980 ◽  
Vol 17 (1) ◽  
pp. 253-258 ◽  
Author(s):  
R. B. Nain ◽  
Kanwar Sen
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Difference Equations ◽  
Generating Functions ◽  
Transition Probability ◽  
Correlated Random Walk ◽  
One Dimensional ◽  
Correlated Random Walks ◽  
Transition Probability Matrices ◽  
Probability Matrices

For correlated random walks a method of transition probability matrices as an alternative to the much-used methods of probability generating functions and difference equations has been investigated in this paper. To illustrate the use of transition probability matrices for computing the various probabilities for correlated random walks, the transition probability matrices for restricted/unrestricted one-dimensional correlated random walk have been defined and used to obtain some of the probabilities.

scholarly journals A Characteristic Polynomial for the Transition Probability Matrix of Correlated Random Walks on a Graph

2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Takashi Komatsu ◽  
Norio Konno ◽  
Iwao Sato
Keyword(s):  
Random Walk ◽  
Zeta Function ◽  
Characteristic Polynomial ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Regular Graphs ◽  
Correlated Random Walk ◽  
Correlated Random Walks ◽  
Transition Probability Matrices ◽  
Probability Matrices

We define a correlated random walk (CRW) induced from the time evolution matrix (the Grover matrix) of the Grover walk on a graph $G$, and present a formula for the characteristic polynomial of the transition probability matrix of this CRW by using a determinant expression for the generalized weighted zeta function of $G$. As an application, we give the spectrum of the transition probability matrices for the CRWs induced from the Grover matrices of regular graphs and semiregular bipartite graphs. Furthermore, we consider another type of the CRW on a graph. 

Some problems on a one-dimensional correlated random walk with various types of barrier

1992 ◽  
Vol 29 (01) ◽  
pp. 196-201 ◽  
Author(s):  
Yuan Lin Zhang
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Correlated Random Walk ◽  
Numerical Examples ◽  
One Dimensional ◽  
Correlated Random Walks ◽  
Expected Duration ◽  
Explicit Expressions

In this paper one-dimensional correlated random walks (CRW) with various types of barrier such as elastic barriers, absorbing barriers and so on are defined, and explicit expressions are derived for the ultimate absorbing probability and expected duration. Some numerical examples to illustrate the effects of correlation are also presented.

Some problems on a one-dimensional correlated random walk with various types of barrier

1992 ◽  
Vol 29 (1) ◽  
pp. 196-201 ◽  
Author(s):  
Yuan Lin Zhang
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Correlated Random Walk ◽  
Numerical Examples ◽  
One Dimensional ◽  
Correlated Random Walks ◽  
Expected Duration ◽  
Explicit Expressions

In this paper one-dimensional correlated random walks (CRW) with various types of barrier such as elastic barriers, absorbing barriers and so on are defined, and explicit expressions are derived for the ultimate absorbing probability and expected duration. Some numerical examples to illustrate the effects of correlation are also presented.

Optimal stopping rules for correlated random walks with a discount

2004 ◽  
Vol 41 (2) ◽  
pp. 483-496 ◽  
Author(s):  
Pieter Allaart
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Optimal Stopping ◽  
Constant Factor ◽  
Stopping Rules ◽  
Correlated Random Walk ◽  
Numerical Examples ◽  
Optimal Rule ◽  
Correlated Random Walks ◽  
Optimal Stopping Rules

Optimal stopping rules are developed for the correlated random walk when future returns are discounted by a constant factor per unit time. The optimal rule is shown to be of dual threshold form: one threshold for stopping after an up-step, and another for stopping after a down-step. Precise expressions for the thresholds are given for both the positively and the negatively correlated cases. The optimal rule is illustrated by several numerical examples.

scholarly journals Zero-one-only process: A correlated random walk with a stochastic ratchet

2014 ◽  
Vol 28 (29) ◽  
pp. 1450201
Author(s):  
Seung Ki Baek ◽  
Hawoong Jeong ◽  
Seung-Woo Son ◽  
Beom Jun Kim
Keyword(s):  
Transport Phenomenon ◽  
Random Walk ◽  
Random Walks ◽  
Stochastic Processes ◽  
Function Method ◽  
Correlated Random Walk ◽  
One Dimensional ◽  
Persistent Random Walk ◽  
The One ◽  
Previous Step

The investigation of random walks is central to a variety of stochastic processes in physics, chemistry and biology. To describe a transport phenomenon, we study a variant of the one-dimensional persistent random walk, which we call a zero-one-only process. It makes a step in the same direction as the previous step with probability p, and stops to change the direction with 1 − p. By using the generating-function method, we calculate its characteristic quantities such as the statistical moments and probability of the first return.

Return probabilities for correlated random walks

1986 ◽  
Vol 23 (1) ◽  
pp. 201-207
Author(s):  
Gillian Iossif
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Integer Lattice ◽  
Asymptotic Estimates ◽  
Correlated Random Walk ◽  
Correlated Random Walks ◽  
Previous Step

A correlated random walk on a d-dimensional integer lattice is studied in which, at any stage, the probabilities of the next step being in the various possible directions depend on the direction of the previous step. Using a renewal argument, asymptotic estimates are obtained for the probability of return to the origin after n steps.

Return probabilities for correlated random walks

1986 ◽  
Vol 23 (01) ◽  
pp. 201-207 ◽  
Author(s):  
Gillian Iossif
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Integer Lattice ◽  
Asymptotic Estimates ◽  
Correlated Random Walk ◽  
Correlated Random Walks ◽  
Previous Step

A correlated random walk on a d-dimensional integer lattice is studied in which, at any stage, the probabilities of the next step being in the various possible directions depend on the direction of the previous step. Using a renewal argument, asymptotic estimates are obtained for the probability of return to the origin after n steps.

Optimal stopping rules for correlated random walks with a discount

2004 ◽  
Vol 41 (02) ◽  
pp. 483-496 ◽  
Author(s):  
Pieter Allaart
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Optimal Stopping ◽  
Constant Factor ◽  
Stopping Rules ◽  
Correlated Random Walk ◽  
Numerical Examples ◽  
Optimal Rule ◽  
Correlated Random Walks ◽  
Optimal Stopping Rules

Optimal stopping rules are developed for the correlated random walk when future returns are discounted by a constant factor per unit time. The optimal rule is shown to be of dual threshold form: one threshold for stopping after an up-step, and another for stopping after a down-step. Precise expressions for the thresholds are given for both the positively and the negatively correlated cases. The optimal rule is illustrated by several numerical examples.

scholarly journals Infinitely divisible random transition probabilities with application to dependent Markov chains

1984 ◽  
Vol 25 (4) ◽  
pp. 463-472
Author(s):  
Peter L. Chesson
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
White Noise ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Transition Rates ◽  
Infinitely Divisible ◽  
Random Transition ◽  
Transition Probability Matrices ◽  
Probability Matrices

AbstractRandom transition probability matrices with stationary independent factors define “white noise” environment processes for Markov chains. Two examples are considered in detail. Such environment processes can be used to construct several Markov chains which are dependent, have the same transition probabilities and are jointly a Markov chain. Transition rates for such processes are evaluated. These results have application to the study of animal movements.

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