Exit times of diffusions

1982 ◽  
pp. 98-105
Author(s):  
Carl Mueller
Keyword(s):  
Exit Times

Exit times of a Brownian particle out of a convection roll

2020 ◽  
Vol 32 (9) ◽  
pp. 092010
Author(s):  
Qingqing Yin ◽  
Yunyun Li ◽  
Fabio Marchesoni ◽  
Tanwi Debnath ◽  
Pulak K. Ghosh
Keyword(s):  
Brownian Particle ◽  
Exit Times ◽  
Convection Roll

scholarly journals On transient Markov processes of Ornstein-Uhlenbeck type

1998 ◽  
Vol 149 ◽  
pp. 19-32 ◽  
Author(s):  
Kouji Yamamuro
Keyword(s):  
Markov Processes ◽  
Lévy Processes ◽  
Transition Probabilities ◽  
Levy Processes ◽  
Exit Times ◽  
Linear Drift ◽  
Lévy Measures ◽  
Drift Terms

Abstract.For Hunt processes on Rd, strong and weak transience is defined by finiteness and infiniteness, respectively, of the expected last exit times from closed balls. Under some condition, which is satisfied by Lévy processes and Ornstein-Uhlenbeck type processes, this definition is expressed in terms of the transition probabilities. A criterion is given for strong and weak transience of Ornstein-Uhlenbeck type processes on Rd, using their Lévy measures and coefficient matrices of linear drift terms. An example is discussed.

scholarly journals THE TWO-TRAIN SEPARATION PROBLEM ON LEVEL TRACK WITH DISCRETE CONTROL

2018 ◽  
Vol 60 (2) ◽  
pp. 137-174
Author(s):  
PHIL HOWLETT
Keyword(s):  
Control Mechanism ◽  
Optimal Strategies ◽  
Discrete Control ◽  
Separation Condition ◽  
Exit Times ◽  
Separation Problem ◽  
Safety Requirement ◽  
Driving Speed ◽  
Optimal Driving

When two trains travel along the same track in the same direction, it is a common safety requirement that the trains must be separated by at least two signals. This means that there will always be at least one clear section of track between the two trains. If the safe-separation condition is violated, then the driver of the following train must adopt a revised strategy that will enable the train to stop at the next signal if necessary. One simple way to ensure safe separation is to define a prescribed set of latest allowed section exit times for the leading train and a corresponding prescribed set of earliest allowed section entry times for the following train. We will find strategies that minimize the total tractive energy required for both trains to complete their respective journeys within the overall allowed journey times and subject to the additional prescribed section clearance times. We assume that the drivers use a discrete control mechanism and show that the optimal driving strategy for each train is defined by a sequence of approximate speedholding phases at a uniquely defined optimal driving speed on each section and that the sequence of optimal driving speeds is a decreasing sequence for the leading train and an increasing sequence for the following train. We illustrate our results by finding optimal strategies and associated speed profiles for both trains in some elementary but realistic examples.

On Brownian exit times from perturbed multi-strips

2019 ◽  
Vol 147 ◽  
pp. 1-5
Author(s):  
M. Lifshits ◽  
A. Nazarov
Keyword(s):  
Exit Times

Exit Times, Moment Problems and Comparison Theorems

2012 ◽  
Vol 38 (4) ◽  
pp. 1365-1372 ◽  
Author(s):  
Patrick McDonald
Keyword(s):  
Comparison Theorems ◽  
Moment Problems ◽  
Exit Times

The Relaxation time for truncated birth-death processes

1987 ◽  
Vol 1 (4) ◽  
pp. 367-381 ◽  
Author(s):  
Julian Keilson ◽  
Ravi Ramaswamy
Keyword(s):  
Relaxation Time ◽  
Exit Time ◽  
Relaxation Times ◽  
Dual Process ◽  
Death Process ◽  
Exit Times ◽  
Initial State ◽  
Death Rates ◽  
Absorbing States ◽  
Birth Death

The relaxation time for an ergodic Markov process is a measure of the time until ergodicity is reached from its initial state. In this paper the relaxation time for an ergodic truncated birth-death process is studied. It is shown that the relaxation time for such a process on states {0,1, …, N} is the quasi-stationary exit time from the set {,2, …, N{0,1,…, N, N + 1} with two-sided absorption at states 0 and N + 1. The existence of such a dual process has been observed by Siegmund [15] for stochastically monotone Markov processes on the real line. Exit times for birth- death processes with two absorbing states are studied and an efficient algorithm for the numerical evaluation of mean exit times is presented. Simple analytical lower bounds for the relaxation times are obtained. These bounds are numerically accessible. Finally, the sensitivity of the relaxation time to variations in birth and death rates is studied.

Limit theorems for suprema, threshold-stopped random variables and last exits of i.i.d. random variables with costs and discounting, with applications to optimal stopping

1992 ◽  
Vol 24 (02) ◽  
pp. 241-266
Author(s):  
Douglas P. Kennedy ◽  
Robert P. Kertz
Keyword(s):  
Optimal Stopping ◽  
Limit Theorems ◽  
Continuous Mapping ◽  
Random Variables ◽  
Exit Times ◽  
Convergence Results ◽  
Process Convergence ◽  
Optimal Stopping Problems ◽  
The Cost ◽  
Linear Cost

For linear-cost-adjusted and geometric-discounted infinite sequences of i.i.d. random variables, point process convergence results are proved as the cost or discounting effect diminishes. These process convergence results are combined with continuous-mapping principles to obtain results on joint convergence of suprema and threshold-stopped random variables, and last-exit times and locations. Applications are made to several classical optimal stopping problems in these settings.

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