A Study of Human Decisions in a Stationary Markov Process With Rewards

1966 ◽  
Author(s):  
Amnon Rapoport
Keyword(s):  
Markov Process ◽  
Stationary Markov Process

On Sieved Orthogonal Polynomials II: Random Walk Polynomials

1986 ◽  
Vol 38 (2) ◽  
pp. 397-415 ◽  
Author(s):  
Jairo Charris ◽  
Mourad E. H. Ismail
Keyword(s):  
Random Walk ◽  
Markov Process ◽  
Orthogonal Polynomials ◽  
Transition Probabilities ◽  
Death Process ◽  
Birth And Death Process ◽  
Stationary Markov Process ◽  
Image Position

A birth and death process is a stationary Markov process whose states are the nonnegative integers and the transition probabilities(1.1)satisfy(1.2)as t → 0. Here we assume βn > 0, δn + 1 > 0, n = 0, 1, …, but δ0 ≦ 0. Karlin and McGregor [10], [11], [12], showed that each birth and death process gives rise to two sets of orthogonal polynomials. The first is the set of birth and death process polynomials {Qn(x)} generated by

Autoregressive logistic processes

1989 ◽  
Vol 26 (03) ◽  
pp. 524-531 ◽  
Author(s):  
Barry C. Arnold ◽  
C. A. Robertson
Keyword(s):  
Markov Process ◽  
Stochastic Model ◽  
Moving Average ◽  
Higher Order ◽  
Invariant Distribution ◽  
Absolutely Continuous ◽  
Joint Distributions ◽  
Moving Average Processes ◽  
Stationary Markov Process

A stochastic model is presented which yields a stationary Markov process whose invariant distribution is logistic. The model is autoregressive in character and is closely related to the autoregressive Pareto processes introduced earlier by Yeh et al. (1988). The model may be constructed to have absolutely continuous joint distributions. Analogous higher-order autoregressive and moving average processes may be constructed.

The minimum of a stationary Markov process superimposed on a U-shaped trend

1969 ◽  
Vol 6 (02) ◽  
pp. 399-408 ◽  
Author(s):  
H.E. Daniels
Keyword(s):  
Markov Process ◽  
Stationary Process ◽  
Probability Distributions ◽  
Asymptotic Independence ◽  
Curved Boundary ◽  
Sample Paths ◽  
Winter Temperatures ◽  
Free Case ◽  
Stationary Markov Process ◽  
The Mean

1. This paper was motivated by some questions of Barnett and Lewis (1967) concerning extreme winter temperatures. The temperature during the winter can be hopefully regarded as generated by a stationary Gaussian process superimposed on a locally U-shaped trend. One is interested in statistical properties of the minimum of sample paths from such a process, and of their excursions below a given level. Equivalently one can consider paths from a stationary process crossing a curved boundary of the same form. Problems of this type are discussed by Cramer and Leadbetter (1967), extensively in the trend-free case and in less detail when a trend is present, following the method initiated by Rice (1945). While results on moments are easy to obtain, explicit results for the actual probability distributions are not usually available. However, in the important case when the level of values of interest is far below the mean, the asymptotic independence of up-crossing times makes it possible to derive simple approximate distributions. (See Cramer and Leadbetter (1967) page 256, Keilson (1966).)

The variance of duration of stay in an absorbing Markov process

1978 ◽  
Vol 15 (02) ◽  
pp. 420-425
Author(s):  
Philip F. Rust
Keyword(s):  
Markov Process ◽  
Infinite Series ◽  
Series Solution ◽  
Initial State ◽  
Duration Of Stay ◽  
Transient States ◽  
Stationary Markov Process ◽  
Absorbing States

Given a stationary Markov process with s transient states and r absorbing states, a matrix infinite series solution is presented for the variance of duration of stay in state j within the interval [0, t), given initial state i. Closed forms are derived for absorbing states, and for transient states if eigenvalues are real and distinct. Several relationships among Markov matrices are presented.

The minimum of a stationary Markov process superimposed on a U-shaped trend

1969 ◽  
Vol 6 (2) ◽  
pp. 399-408 ◽  
Author(s):  
H.E. Daniels
Keyword(s):  
Markov Process ◽  
Stationary Process ◽  
Probability Distributions ◽  
Asymptotic Independence ◽  
Curved Boundary ◽  
Sample Paths ◽  
Winter Temperatures ◽  
Free Case ◽  
Stationary Markov Process ◽  
The Mean

1. This paper was motivated by some questions of Barnett and Lewis (1967) concerning extreme winter temperatures. The temperature during the winter can be hopefully regarded as generated by a stationary Gaussian process superimposed on a locally U-shaped trend. One is interested in statistical properties of the minimum of sample paths from such a process, and of their excursions below a given level. Equivalently one can consider paths from a stationary process crossing a curved boundary of the same form. Problems of this type are discussed by Cramer and Leadbetter (1967), extensively in the trend-free case and in less detail when a trend is present, following the method initiated by Rice (1945). While results on moments are easy to obtain, explicit results for the actual probability distributions are not usually available. However, in the important case when the level of values of interest is far below the mean, the asymptotic independence of up-crossing times makes it possible to derive simple approximate distributions. (See Cramer and Leadbetter (1967) page 256, Keilson (1966).)

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