scholarly journals Random walk radiosity with generalized absorption probabilities

2002 ◽  
Author(s):  
M. Sbert
Keyword(s):  
Random Walk ◽  
Absorption Probabilities

On the absorption probabilities and mean time for absorption for discrete Markov chains

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nikolaos Halidias
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Chains ◽  
Generating Function ◽  
Discrete Time ◽  
Probability Generating Function ◽  
The Mean ◽  
Mean Time ◽  
Absorption Probabilities

Abstract In this note we study the probability and the mean time for absorption for discrete time Markov chains. In particular, we are interested in estimating the mean time for absorption when absorption is not certain and connect it with some other known results. Computing a suitable probability generating function, we are able to estimate the mean time for absorption when absorption is not certain giving some applications concerning the random walk. Furthermore, we investigate the probability for a Markov chain to reach a set A before reach B generalizing this result for a sequence of sets A 1 , A 2 , … , A k {A_{1},A_{2},\dots,A_{k}} .

A Note on Absorption Probabilities for a Random Walk Between a Reflecting and an Absorbing Barrier

1969 ◽  
Vol 6 (01) ◽  
pp. 224-226
Author(s):  
J.C. Hardin ◽  
A.L. Sweet
Keyword(s):  
Random Walk ◽  
Generating Functions ◽  
Absorption Probabilities ◽  
Explicit Expressions

Generating functions for the absorption probabilities for a random walk on the integers {0,1, …, b}, where 0 is an absorbing barrier and b a semi-reflecting barrier have been obtained by Weesakul [1] and Neuts [2]. However, determination of explicit expressions for the absorption probabilities from the generating functions is generally quite difficult. In this note, two cases where this is possible are presented.

A two-dimensional random walk in the presence of a partially reflecting barrier

1974 ◽  
Vol 11 (01) ◽  
pp. 199-205
Author(s):  
Noel Cressie
Keyword(s):  
Random Walk ◽  
Two Dimensional ◽  
Absorption Probabilities

A general two-dimensional random walk is considered with a barrier along the y-axis. Absorption probabilities are derived when the barrier is absorbing, and when it is semi-reflecting.

A two-dimensional random walk in the presence of a partially reflecting barrier

1974 ◽  
Vol 11 (1) ◽  
pp. 199-205 ◽  
Author(s):  
Noel Cressie
Keyword(s):  
Random Walk ◽  
Two Dimensional ◽  
Absorption Probabilities

A general two-dimensional random walk is considered with a barrier along the y-axis. Absorption probabilities are derived when the barrier is absorbing, and when it is semi-reflecting.

Bounds on Absorption Probabilities for the m-Dimensional Random Walk

1977 ◽  
Vol 72 (357) ◽  
pp. 154
Author(s):  
William E. Wecker ◽  
Thomas E. Morton
Keyword(s):  
Random Walk ◽  
Absorption Probabilities

A Note on Absorption Probabilities for a Random Walk Between a Reflecting and an Absorbing Barrier

1969 ◽  
Vol 6 (1) ◽  
pp. 224-226 ◽  
Author(s):  
J.C. Hardin ◽  
A.L. Sweet
Keyword(s):  
Random Walk ◽  
Generating Functions ◽  
Absorption Probabilities ◽  
Explicit Expressions

Generating functions for the absorption probabilities for a random walk on the integers {0,1, …, b}, where 0 is an absorbing barrier and b a semi-reflecting barrier have been obtained by Weesakul [1] and Neuts [2]. However, determination of explicit expressions for the absorption probabilities from the generating functions is generally quite difficult. In this note, two cases where this is possible are presented.

Wald's identity and absorption probabilities for two-dimensional random walks

1965 ◽  
Vol 61 (3) ◽  
pp. 747-762 ◽  
Author(s):  
V. D. Barnett
Keyword(s):  
Random Walk ◽  
Double Series ◽  
Moment Generating Function ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Region ◽  
Discrete Random Variables ◽  
Image Position ◽  
Wald's Identity ◽  
Absorption Probabilities

SummarySuppose a particle executes a random walk on a two-dimensional square lattice, starting at the origin. The position of the particle after n steps of the walk is Xn = (Xl, n, X2n), whereand we will assume that the Yi are independent bivariate discrete random variables with common moment generating function (m.g.f.)where a, b, c and d are non-negative. We assume further that (i) pi, j is non-zero for some finite positive and negative i, and some finite positive and negative j (− a ≤ i ≤ b, − c ≤ jd), such values of i and j including – a, b and – c, d, respectively, whenever a, b, c or d is finite, and (ii) the double series defining Φ(α, β) is convergent at least in some finite region D, of the real (α, β) plane, which includes the origin.

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