An Integral Equation Method for the First-Passage Problem in Random Vibration

1984 ◽  
Vol 51 (3) ◽  
pp. 674-679 ◽  
Author(s):  
P. H. Madsen ◽  
S. Krenk
Keyword(s):  
Integral Equation ◽  
Random Vibration ◽  
Integral Equation Method ◽  
Nonstationary Process ◽  
Alternative Methods ◽  
Approximation Formula ◽  
First Passage ◽  
Special Cases ◽  
Nonstationary Stochastic Process ◽  
First Passage Problem

The first-passage problem for a nonstationary stochastic process is formulated as an integral identity, which produces known bounds and series expansions as special cases, while approximation of the kernel leads to an integral equation for the first-passage probability density function. An accurate, explicit approximation formula for the kernel is derived, and the influence of uni or multi modal frequency content of the process is investigated. Numerical results provide comparisons with simulation results and alternative methods for narrow band processes, and also the case of a multimodal, nonstationary process is dealt with.

Moments of the first-passage time of a Wiener process with drift between two elastic barriers

1995 ◽  
Vol 32 (4) ◽  
pp. 1007-1013 ◽  
Author(s):  
Marco Dominé
Keyword(s):  
Wiener Process ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
One Dimensional ◽  
Special Cases ◽  
Backward Equation ◽  
The One ◽  
First Passage Problem ◽  
Reflecting Barriers

The first-passage problem for the one-dimensional Wiener process with drift in the presence of elastic boundaries is considered. We use the Kolmogorov backward equation with corresponding boundary conditions to derive explicit closed-form expressions for the expected value and the variance of the first-passage time. Special cases with pure absorbing and/or reflecting barriers arise for a certain choice of a parameter constellation.

scholarly journals Improved Integral Equation Solution for the First Passage Time of Leaky Integrate-and-Fire Neurons

2011 ◽  
Vol 23 (2) ◽  
pp. 421-434 ◽  
Author(s):  
Yi Dong ◽  
Stefan Mihalas ◽  
Ernst Niebur
Keyword(s):  
Integral Equation ◽  
First Passage Time ◽  
Integral Equation Method ◽  
Passage Time ◽  
First Passage ◽  
Small Noise ◽  
Numerical Errors ◽  
Integrate And Fire ◽  
Probability Current ◽  
The Mean

An accurate calculation of the first passage time probability density (FPTPD) is essential for computing the likelihood of solutions of the stochastic leaky integrate-and-fire model. The previously proposed numerical calculation of the FPTPD based on the integral equation method discretizes the probability current of the voltage crossing the threshold. While the method is accurate for high noise levels, we show that it results in large numerical errors for small noise. The problem is solved by analytically computing, in each time bin, the mean probability current. Efficiency is further improved by identifying and ignoring time bins with negligible mean probability current.

Boundary Integral Equation Formulation in Generalized Linear Thermo-Viscoelasticity With Rheological Volume

2002 ◽  
Author(s):  
Ahmed S. El-Karamany
Keyword(s):  
Integral Equation ◽  
Rheological Properties ◽  
Boundary Integral Equation ◽  
General Model ◽  
Relaxation Times ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Integral Equation Formulation ◽  
Special Cases ◽  
The Given

A general model of generalized linear thermo-viscoelasticity for isotropic material is established taking into consideration the rheological properties of the volume. As special cases the corresponding equations for the coupled thermo-viscoelasticity and the generalized thermo-viscoelasticity with one (Lord-Shulman theory) or with two relaxation times (Green-Lindsay theory) are obtained. The cases of thermo-viscoelasticity ignoring the rheological properties of volume can be obtained from the given model. The equations of the corresponding thermoelasticity theories result from the given model as special cases. A formulation of the boundary integral equation method, fundamental solutions of the corresponding differential equations are obtained and the dynamic reciprocity theorem is derived for this general model. Generalizations of Somiliana’s –Green and Maysels formulas are obtained. An example illustrating the BIE formulation is given. Special emphasis is given to the representation of primary fields, namely temperature and displacement.

SOME RESULTS ON A NEW CLASS OF SHOCK MODELS

2010 ◽  
Vol 27 (04) ◽  
pp. 503-515
Author(s):  
ALAGAR RANGAN ◽  
AYŞE TANSU
Keyword(s):  
Failure Time ◽  
System Failure ◽  
First Passage ◽  
New Class ◽  
Optimal Replacement ◽  
Random Threshold ◽  
Shock Models ◽  
Special Cases ◽  
Replacement Problem ◽  
First Passage Problem

Traditional shock models view system failure time as a first passage problem. Yeh Lam proposed a new class of models called δ-shock models in which failure was dependent on the frequency of shocks. The present work generalizes Yeh Lam's results for renewal shock arrivals and random threshold. Several special cases and an optimal replacement problem are also discussed.

Moments of the first-passage time of a Wiener process with drift between two elastic barriers

1995 ◽  
Vol 32 (04) ◽  
pp. 1007-1013 ◽  
Author(s):  
Marco Dominé
Keyword(s):  
Wiener Process ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
One Dimensional ◽  
Special Cases ◽  
Backward Equation ◽  
The One ◽  
First Passage Problem ◽  
Reflecting Barriers

The first-passage problem for the one-dimensional Wiener process with drift in the presence of elastic boundaries is considered. We use the Kolmogorov backward equation with corresponding boundary conditions to derive explicit closed-form expressions for the expected value and the variance of the first-passage time. Special cases with pure absorbing and/or reflecting barriers arise for a certain choice of a parameter constellation.

Sign in / Sign up

Export Citation Format

Share Document