First-passage problem of strongly nonlinear stochastic oscillators with external and internal resonances

AbstractWe explore the first passage problem for sticky reflecting diffusion processes with double exponential jumps. The joint Laplace transform of the first passage time to an upper level and the corresponding overshoot is studied. In particular, explicit solutions are presented when the diffusion part is driven by a drifted Brownian motion and by an Ornstein–Uhlenbeck process.

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The density of interfaces: a new first-passage problem

Journal of Applied Probability ◽

10.1017/s0021900200044612 ◽

1993 ◽

Vol 30 (04) ◽

pp. 851-862 ◽

Cited By ~ 1

Author(s):

L. Chayes ◽

C. Winfield

Keyword(s):

Correlation Length ◽

First Passage Time ◽

Passage Time ◽

Scaling Behavior ◽

First Passage Percolation ◽

First Passage ◽

Site Percolation ◽

Percolation Problem ◽

First Passage Problem

We introduce and study a novel type of first-passage percolation problem onwhere the associated first-passage time measures the density of interface between two types of sites. If the types, designated + and –, are independently assigned their values with probabilitypand (1 —p) respectively, we show that the density of interface is non-zero provided that both species are subcritical with regard to percolation, i.e.pc>p> 1 –pc.Furthermore, we show that asp↑pcorp↓ (1 –pc), the interface density vanishes with scaling behavior identical to the correlation length of the site percolation problem.

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Efficient solution of the first passage problem by Path Integration for normal and Poissonian white noise

Probabilistic Engineering Mechanics ◽

10.1016/j.probengmech.2015.06.007 ◽

2015 ◽

Vol 41 ◽

pp. 121-128 ◽

Cited By ~ 13

Author(s):

Christian Bucher ◽

Mario Di Paola

Keyword(s):

White Noise ◽

Path Integration ◽

Efficient Solution ◽

First Passage ◽

First Passage Problem

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The first-passage problem for diffusion through a cylindrical pore with sticky walls

The European Physical Journal E ◽

10.1140/epje/i2009-10529-0 ◽

2009 ◽

Vol 30 (4) ◽

Cited By ~ 7

Author(s):

N. A. Licata ◽

S. W. Grill

Keyword(s):

First Passage ◽

Cylindrical Pore ◽

First Passage Problem

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

Journal of Applied Probability ◽

10.2307/3215214 ◽

1995 ◽

Vol 32 (4) ◽

pp. 1007-1013 ◽

Cited By ~ 17

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.

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Some Renewal Theorems with Application to a First Passage Problem

The Annals of Mathematical Statistics ◽

10.1214/aoms/1177699465 ◽

1966 ◽

Vol 37 (3) ◽

pp. 699-710 ◽

Cited By ~ 37

Author(s):

C. C. Heyde

Keyword(s):

First Passage ◽

First Passage Problem

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

Journal of Applied Mechanics ◽

10.1115/1.3167691 ◽

1984 ◽

Vol 51 (3) ◽

pp. 674-679 ◽

Cited By ~ 53

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.

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