First Exit Time Problem

2012 ◽  
Keyword(s):  
Exit Time ◽  
First Exit Time ◽  
Time Problem

First Exit Time Problem

2011 ◽  
pp. 521-523 ◽  
Author(s):  
Christos H. Skiadas ◽  
Charilaos Skiadas
Keyword(s):  
Exit Time ◽  
First Exit Time ◽  
Time Problem

scholarly journals AN INTEGRAL EQUATION FOR THE DISTRIBUTION OF THE FIRST EXIT TIME OF A REFLECTED BROWNIAN MOTION

2009 ◽  
Vol 50 (4) ◽  
pp. 445-454 ◽  
Author(s):  
VICTOR DE-LA-PEÑA ◽  
GERARDO HERNÁNDEZ-DEL-VALLE ◽  
CARLOS G. PACHECO-GONZÁLEZ
Keyword(s):  
Integral Equation ◽  
Brownian Motion ◽  
First Passage Time ◽  
Exit Time ◽  
Numerical Procedure ◽  
Passage Time ◽  
Reflected Brownian Motion ◽  
First Exit Time ◽  
Time Problem ◽  
First Passage Time Problem

AbstractReflected Brownian motion is used in areas such as physiology, electrochemistry and nuclear magnetic resonance. We study the first-passage-time problem of this process which is relevant in applications; specifically, we find a Volterra integral equation for the distribution of the first time that a reflected Brownian motion reaches a nondecreasing barrier. Additionally, we note how a numerical procedure can be used to solve the integral equation.

On the first-exit time problem for temporally homogeneous Markov processes

1976 ◽  
Vol 13 (1) ◽  
pp. 39-48 ◽  
Author(s):  
Henry C. Tuckwell
Keyword(s):  
Recurrence Relations ◽  
Diffusion Processes ◽  
Transition Probability ◽  
Exit Time ◽  
Model Neuron ◽  
Kolmogorov Equation ◽  
First Exit Time ◽  
Transition Probability Density ◽  
Homogeneous Markov Process ◽  
Time Problem

Using an integral equation of Darling and Siegert in conjunction with the backward Kolmogorov equation for the transition probability density function, recurrence relations are derived for the moments of the time of first exit of a temporally homogeneous Markov process from a set in the phase space. The results, which are similar to those for diffusion processes, are used to find the expectation of the time between impulses of a Stein model neuron.

On the first-exit time problem for temporally homogeneous Markov processes

1976 ◽  
Vol 13 (01) ◽  
pp. 39-48 ◽  
Author(s):  
Henry C. Tuckwell
Keyword(s):  
Recurrence Relations ◽  
Diffusion Processes ◽  
Transition Probability ◽  
Exit Time ◽  
Model Neuron ◽  
Kolmogorov Equation ◽  
First Exit Time ◽  
Transition Probability Density ◽  
Homogeneous Markov Process ◽  
Time Problem

Using an integral equation of Darling and Siegert in conjunction with the backward Kolmogorov equation for the transition probability density function, recurrence relations are derived for the moments of the time of first exit of a temporally homogeneous Markov process from a set in the phase space. The results, which are similar to those for diffusion processes, are used to find the expectation of the time between impulses of a Stein model neuron.

n-point, win-by-k games

1989 ◽  
Vol 26 (4) ◽  
pp. 807-814 ◽  
Author(s):  
Kyle Siegrist
Keyword(s):  
Exit Time ◽  
Bernoulli Trials ◽  
Expected Number ◽  
First Exit Time ◽  
World Series ◽  
Time Space ◽  
Gambler’S Ruin ◽  
Gambler's Ruin Problem ◽  
Positive Integers ◽  
Made In

Consider a sequence of Bernoulli trials between players A and B in which player A wins each trial with probability p∈ [0, 1]. For positive integers n and k with k ≦ n, an (n, k) contest is one in which the first player to win at least n trials and to be ahead of his opponent by at least k trials wins the contest. The (n, 1) contest is the Banach match problem and the (n, n) contest is the gambler's ruin problem. Many real contests (such as the World Series in baseball and the tennis game) have an (n, 1) or an (n, 2) format. The (n, k) contest is formulated in terms of the first-exit time of the graph of a random walk from a certain region of the state-time space. Explicit results are obtained for the probability that player A wins an (n, k) contest and the expected number of trials in an (n, k) contest. Comparisons of (n, k) contests are made in terms of the probability that the stronger player wins and the expected number of trials.

scholarly journals A variation on the Donsker–Varadhan inequality for the principal eigenvalue

2017 ◽  
Vol 473 (2204) ◽  
pp. 20160877
Author(s):  
Jianfeng Lu ◽  
Stefan Steinerberger
Keyword(s):  
Lower Bound ◽  
Exit Time ◽  
Principal Eigenvalue ◽  
Short Paper ◽  
First Eigenvalue ◽  
Drift Diffusion ◽  
First Exit Time ◽  
The First Eigenvalue ◽  
Order Elliptic Operator ◽  
The Mean

The purpose of this short paper is to give a variation on the classical Donsker–Varadhan inequality, which bounds the first eigenvalue of a second-order elliptic operator on a bounded domain Ω by the largest mean first exit time of the associated drift–diffusion process via λ 1 ≥ 1 sup x ∈ Ω E x τ Ω c . Instead of looking at the mean of the first exit time, we study quantiles: let d p , ∂ Ω : Ω → R ≥ 0 be the smallest time t such that the likelihood of exiting within that time is p , then λ 1 ≥ log ( 1 / p ) sup x ∈ Ω d p , ∂ Ω ( x ) . Moreover, as p → 0 , this lower bound converges to λ 1 .

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