A random walk problem with correlation

1972 ◽  
Vol 9 (2) ◽  
pp. 436-440 ◽  
Author(s):  
A. D. Proudfoot ◽  
D. G. Lampard
Keyword(s):  
Random Walk ◽  
Green’S Function ◽  
Green's Function ◽  
Generating Functions ◽  
Transition Probability ◽  
Higher Order ◽  
Order Transition ◽  
Probability Generating Functions ◽  
Discrete Domain

The higher-order transition probability generating functions for a random-walk with correlation between steps is calculated as a discrete-domain Green's function.

A random walk problem with correlation

1972 ◽  
Vol 9 (02) ◽  
pp. 436-440 ◽  
Author(s):  
A. D. Proudfoot ◽  
D. G. Lampard
Keyword(s):  
Random Walk ◽  
Green’S Function ◽  
Green's Function ◽  
Generating Functions ◽  
Transition Probability ◽  
Higher Order ◽  
Order Transition ◽  
Probability Generating Functions ◽  
Discrete Domain

The higher-order transition probability generating functions for a random-walk with correlation between steps is calculated as a discrete-domain Green's function.

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.

On some classes of population-size-dependent Galton–Watson processes

1985 ◽  
Vol 22 (01) ◽  
pp. 25-36
Author(s):  
Reinhard Höpfner
Keyword(s):  
Population Size ◽  
Lower Bounds ◽  
Generating Functions ◽  
Transition Probability ◽  
Limit Distributions ◽  
Size Dependent ◽  
Probability Generating Functions ◽  
Iteration Methods ◽  
Functional Iteration

Some classes of population-size-dependent Galton–Watson processes {Z(t)} t=0,1, …, whose transition probability generating functions allow for certain upper or lower bounds, can be treated by means of functional iteration methods. Criteria for almost certain extinction are obtained as well as gammatype limit distributions for Z(t)/t as t → ∞ the results can be stated under conditions on moments of the reproduction distributions.

scholarly journals Some results using general moment functions

1969 ◽  
Vol 10 (3-4) ◽  
pp. 429-441 ◽  
Author(s):  
Walter L. Smith
Keyword(s):  
Random Walk ◽  
Generating Functions ◽  
Random Variables ◽  
Closure Property ◽  
Probability Generating Functions ◽  
Moment Functions ◽  
Result Theorem ◽  
Independent And Identically Distributed

SummaryLet {Xn} be a sequence fo independent and identically distributed random variables such that 0 <μ = εXn ≦ + ∞ and write Sn = X1+X2+ … +Xn. Letv ≧ 0 be an integer and let M(x) be a non-decreasing function of x ≧ 0 such that M(x)/x is non-increasing and M(0) > 0. Then if ε|X1νM(|X1|) < ∞ and μ < ∞ it follows that ε|Sn|νM(|Sn|) ~ (nμ)vM(nμ) as n → ∞. If μ = ∞ (ν = 0) then εM(|Sn|) = 0(n). A variety of results stem from this main theorem (Theorem 2), concerning a closure property of probability generating functions and a random walk result (Theorem 1) connected with queues.

On some classes of population-size-dependent Galton–Watson processes

1985 ◽  
Vol 22 (1) ◽  
pp. 25-36 ◽  
Author(s):  
Reinhard Höpfner
Keyword(s):  
Population Size ◽  
Lower Bounds ◽  
Generating Functions ◽  
Transition Probability ◽  
Limit Distributions ◽  
Size Dependent ◽  
Probability Generating Functions ◽  
Iteration Methods ◽  
Functional Iteration

Some classes of population-size-dependent Galton–Watson processes {Z(t)}t=0,1, …, whose transition probability generating functions allow for certain upper or lower bounds, can be treated by means of functional iteration methods. Criteria for almost certain extinction are obtained as well as gammatype limit distributions for Z(t)/t as t → ∞ the results can be stated under conditions on moments of the reproduction distributions.

scholarly journals Scaling limit of the loop-erased random walk Green’s function

2015 ◽  
Vol 166 (1-2) ◽  
pp. 271-319 ◽  
Author(s):  
Christian Beneš ◽  
Gregory F. Lawler ◽  
Fredrik Viklund
Keyword(s):  
Random Walk ◽  
Green’S Function ◽  
Green's Function ◽  
Scaling Limit

Green's Function Approach to Crossover Properties for Interaction Parameters of an N-Layer Ferroelectric Thin Film

2010 ◽  
Vol 152-153 ◽  
pp. 116-120
Author(s):  
Zhao Xin Lu ◽  
Bao Hua Teng ◽  
Xin Yang
Keyword(s):  
Thin Film ◽  
Phase Diagram ◽  
Green’S Function ◽  
Green's Function ◽  
Ferroelectric Thin Film ◽  
Higher Order ◽  
Interaction Parameters ◽  
Mean Field Approximation ◽  
Decoupling Approximation ◽  
Dominant Phase

Utilizing the higher order decoupling approximation to the Fermi-type Green’s function, crossover properties of interaction parameters of an n-layer ferroelectric thin film from the ferroelectric-dominant phase diagram (FPD) to the paraelectric-dominant phase diagram (PPD) are investigated on the basis of the transverse Ising model. The curved surfaces for crossover values of interaction parameters of a thin film with certain layers are constructed in the three-dimensional parameter space. Because both the z-component <Sz> (the polarization) and the transverse component <Sx> of the spin are further included in the eigenfrequency, the results are in agreement with that of the effective-field theory with correlations to some extent. It shows that the higher order decoupling approximation diminishes the ferroelectric feature of a ferroelectric thin film compared with the usual mean-field approximation.

Second- and higher-order resonant gratings with gain or loss-Part 1: Green's function analysis

2000 ◽  
Vol 36 (12) ◽  
pp. 1421-1430 ◽  
Author(s):  
A.M. Shams-Zadeh-Amiri ◽  
Jin Hong ◽  
Xun Li ◽  
Wei-Ping Huang
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Analysis ◽  
Higher Order
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