Level-crossing probabilities and first-passage times for linear processes

Discrete time-series models are commonly used to represent economic and physical data. In decision making and system control, the first-passage time and level-crossing probabilities of these processes against certain threshold levels are important quantities. In this paper, we apply an integral-equation approach together with the state-space representations of time-series models to evaluate level-crossing probabilities for the AR(p) and ARMA(1,1) models and the mean first passage time for AR(p) processes. We also extend Novikov's martingale approach to ARMA(p,q) processes. Numerical schemes are used to solve the integral equations for specific examples.

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Level-crossing probabilities and first-passage times for linear processes

Advances in Applied Probability ◽

10.1239/aap/1086957589 ◽

2004 ◽

Vol 36 (2) ◽

pp. 643-666 ◽

Cited By ~ 5

Author(s):

Gopal K. Basak ◽

Kwok-Wah Remus Ho

Keyword(s):

Time Series ◽

First Passage Time ◽

Passage Time ◽

Time Series Models ◽

System Control ◽

Level Crossing ◽

First Passage ◽

Linear Processes ◽

Integral Equation Approach ◽

Crossing Probabilities

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First passage time and crossing probabilities of some correlated processes

10.14711/thesis-b645959 ◽

1999 ◽

Author(s):

Kwok Wah Ho

Keyword(s):

First Passage Time ◽

Passage Time ◽

First Passage ◽

Crossing Probabilities

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On the level crossing of multi-dimensional delayed renewal processes

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/s1048953397000415 ◽

1997 ◽

Vol 10 (4) ◽

pp. 355-361 ◽

Cited By ~ 20

Author(s):

Jewgeni H. Dshalalow

Keyword(s):

Renewal Process ◽

Stochastic Models ◽

First Passage Time ◽

Passage Time ◽

The Other ◽

Renewal Processes ◽

Active Components ◽

Level Crossing ◽

First Passage ◽

Informal Discussion

The paper studies the behavior of an (l+3)th-dimensional, delayed renewal process with dependent components, the first three (called active) of which are to cross one of their respective thresholds. More specifically, the crossing takes place when at least one of the active components reaches or exceeds its assigned level. The values of the other two active components, as well as the rest of the components (passive), are to be registered. The analysis yields the joint functional of the crossing level and other characteristics (some of which can be interpreted as the first passage time) in a closed form, refining earlier results of the author. A brief, informal discussion of various applications to stochastic models is presented.

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Comparison of Jump-Diffusion Parameters Using Passage Times Estimation

Journal of Applied Mathematics ◽

10.1155/2014/975418 ◽

2014 ◽

Vol 2014 ◽

pp. 1-5 ◽

Cited By ~ 1

Author(s):

K. Khaldi ◽

K. Djeddour ◽

S. Meddahi

Keyword(s):

Time Series ◽

First Passage Time ◽

Jump Diffusion ◽

Passage Time ◽

Share Price ◽

First Passage ◽

Diffusion Parameters ◽

Stochastic Jump ◽

Moments Method ◽

Passage Times

The main purposes of this paper are two contributions: (1) it presents a new method, which is the first passage time generalized for all passage times (PT method), in order to estimate the parameters of stochastic jump-diffusion process. (2) It compares in a time series model, share price of gold, the empirical results of the estimation and forecasts obtained with the PT method and those obtained by the moments method applied to the MJD model.

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Mean First Passage Time for the ESTAR Model Using the Integral Equation Approach and Its Applications

Journal of Statistical Theory and Practice ◽

10.1080/15598608.2013.814379 ◽

2014 ◽

Vol 8 (4) ◽

pp. 559-577

Author(s):

Heni Puspaningrum ◽

Yan-Xia Lin ◽

Chandra Gulati

Keyword(s):

Integral Equation ◽

First Passage Time ◽

Passage Time ◽

Mean First Passage Time ◽

Equation Approach ◽

First Passage ◽

Integral Equation Approach

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First-Passage Time Properties of Correlated Time Series with Scale-Invariant Behavior and with Crossovers in the Scaling

Time Series Analysis and Forecasting - Contributions to Statistics ◽

10.1007/978-3-319-28725-6_7 ◽

2016 ◽

pp. 89-102 ◽

Cited By ~ 1

Author(s):

Pedro Carpena ◽

Ana V. Coronado ◽

Concepción Carretero-Campos ◽

Pedro Bernaola-Galván ◽

Plamen Ch. Ivanov

Keyword(s):

Time Series ◽

First Passage Time ◽

Passage Time ◽

Scale Invariant ◽

First Passage

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First passage time for the state of exact chemical equilibrium

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19800777 ◽

1980 ◽

Vol 45 (3) ◽

pp. 777-782 ◽

Cited By ~ 1

Author(s):

Milan Šolc

Keyword(s):

Chemical Equilibrium ◽

First Passage Time ◽

Passage Time ◽

The State ◽

Recurrence Time ◽

First Passage ◽

First Order ◽

The Mean ◽

Passage Times ◽

Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

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