Stratonovich model driven by dichotomous noise: Mean first passage time

Behn, Ulrich; Schiele, K.

doi:10.1007/bf01453799

Cited by 14 publications

(5 citation statements)

References 24 publications

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“…[17,61,62] (and also Refs. [63,64] for the related problem of the mean-first passage time), the problem of dichotomous flows with unstable critical points was generally not approached. We have recently made progress towards identifying the source of spurious divergences that arise in the usual analytical treatment of the problem, see Refs.…”

Section: A Generalitiesmentioning

confidence: 99%

“…However, for general dichotomous flows one can obtain exact results, using various approaches and techniques (backward equations, stochastic trajectory counting and analysis), see Refs. [63,64,121,122,123,124,125,126,127,128,129,130,131,132,133].…”

Section: E Stochastic Stokes' Driftmentioning

confidence: 99%

“…This is the main reason why, with a few exceptions, see Refs [17,61,62]. (and also Refs [63,64]. for the related problem of the mean-first passage time), the problem of dichotomous flows with unstable critical points was generally not approached.…”

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confidence: 99%

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Dichotomous Markov Noise: Exact Results for Out-of-Equilibrium Systems

Bena

2006

Int. J. Mod. Phys. B

136

144

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Nonequilibrium systems driven by additive or multiplicative dichotomous Markov noise appear in a wide variety of physical and mathematical models. We review here some prototypical examples, with an emphasis on analytically-solvable situations. In particular, it has escaped attention till recently that the standard results for the long-time properties of such systems cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present a few relevant applications -the hypersensitive transport, the rocking ratchet, and the stochastic Stokes' drift. These results reinforce the impression that dichotomous noise can be put on a par with Gaussian white noise as far as obtaining analytical results is concerned. They convincingly illustrate the interplay between noise and nonlinearity in generating nontrivial behaviors of nonequilibrium systems and point to various practical applications.

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Section: A Generalitiesmentioning

confidence: 99%

Section: E Stochastic Stokes' Driftmentioning

confidence: 99%

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Dichotomous Markov Noise: Exact Results for Out-of-Equilibrium Systems

Bena

2006

Int. J. Mod. Phys. B

136

144

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“…The RTP model is in some sense an amalgamation of ballistic motion and Brownian motion as by tuning the parameters R and v, one can go from a pure ballistic particle (R → 0) to a pure Brownian particle (R → ∞ and v → ∞ keeping v 2 /R fixed). In the physics literature the telegraphic noise and the RTP process have been studied in various settings starting from persistent Brownian motion, electromagnetic theory, optics, and Lorentz gas to polymers [35][36][37][38][39][40][41][42][43]. The model has gained renewed interest in recent years due to its applicability in mimicking the movement of E. coli [32].…”

Section: Introductionmentioning

confidence: 99%

Run-and-tumble particle in inhomogeneous media in one dimension

Singh¹,

Sabhapandit²,

Kundu³

2020

J. Stat. Mech.

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“…where Prob( ) is given in (3). The boundary conditions necessary to integrate (5) depend on the location of the interval Iand will be specified in the following.…”

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confidence: 99%

Mean first-passage time for systems driven by pre-Gaussian noise: Natural boundary conditions

1993

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In order to determine the mean first-passage time for systems driven by a superposition of suitably scaled independent dichotomous Markovian processes (pre-Gaussian noise), the well-known absorbing boundary conditions must be complemented in the generic case by a novel type of natural boundary conditions. We treat explicitly a linear stochastic Aow for the superposition of up to five dichotomous processes and compare the analytic results with a digital simulation for these processes and an Ornstein-Uhlenbeck process.

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Stratonovich model driven by dichotomous noise: Mean first passage time

Cited by 14 publications

References 24 publications

Dichotomous Markov Noise: Exact Results for Out-of-Equilibrium Systems

Dichotomous Markov Noise: Exact Results for Out-of-Equilibrium Systems

Run-and-tumble particle in inhomogeneous media in one dimension

Mean first-passage time for systems driven by pre-Gaussian noise: Natural boundary conditions

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