Noise in hysteretic systems and stochastic processes on graphs

Freidlin, Mark; Mayergoyz, I.D.; Pfeiffer, R.

doi:10.1103/physreve.62.1850

Cited by 16 publications

(14 citation statements)

References 15 publications

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“…Formula (53) a direct consequence of the symmetric Itô-Tanaka formula (32). After a one-to-one change of variable, if ϕ belongs to BV, then it is easily checked that R ϕ ′ ( dx)k(x) = R ϕ ′ ( dx)k(F −1 (x)) dx for any bounded, measurable function k. The measure µ is then computed with Lemma 2.1 in [52] which asserts the existence of h, the previous change of variable and the relation L…”

Section: Spatial Change Of Variablementioning

confidence: 99%

On the constructions of the skew Brownian motion

Lejay¹

2006

Probab. Surveys

190

219

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This article summarizes the various ways one may use to construct the Skew Brownian motion, and shows their connections. Recent applications of this process in modelling and numerical simulation motivates this survey. This article ends with a brief account of related results, extensions and applications of the Skew Brownian motion.Comment: Published at http://dx.doi.org/10.1214/154957807000000013 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Section: Spatial Change Of Variablementioning

confidence: 99%

On the constructions of the skew Brownian motion

Lejay¹

2006

Probab. Surveys

190

219

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“…In this paper, we will approximate the output of the static rectangular hysteresis operator with the function that satisfies the following first order in time-differential equation: (2) subject to some initial condition . Here, the function simply indicates the staircase interface on the Preisach plane at time zero.…”

Section: Dynamic Approximation Of Rectangular Hysteresis Loopsmentioning

confidence: 99%

“…For continuous time diffusion-type stochastic processes, solutions were formulated by noting that the problem of switching of a rectangular hysteresis loop can be posed as an exit problem of stochastic differential equation (SDE) theory. More recently, the formalism of SDEs was employed to analyze rectangular loops driven by stochastic inputs by posing the problem as a stochastic process on graphs [2].…”

Section: Introductionmentioning

confidence: 99%

Dynamic approximation of rectangular loops and aftereffect

Korman

2003

IEEE Trans. Magn.

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This paper presents a new approach to model hysteresis and aftereffect phenomena. A dynamic approximation of rectangular hysteresis loops is employed that leads to the representation of the input-output relationship as a first-order dynamical system driven by white noise. Closed-form expressions are derived for the output of rectangular loops in terms of convolution-type integrals. The formalism allows one to circumvent some of the mathematical challenges associated with history-dependent switching of rectangular hysteresis loops driven by stochastic processes.

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“…Inserting the controlled diffusion (4.2) into equation (2.7), the probability of abandonment is given by the coupled equations 6) where τ = T − t. These particular boundary conditions are mathematically analogous to hysteresis problem in physics solved by Freidlin et al (2000). As in the previous section, the solution to the coupled equations (4.5)-(4.6) depends on the firm's control strategy.…”

Section: Abandonment Probabilitymentioning

confidence: 99%

Optimal regulatory control of early contract termination

Evatt¹,

Johnson²,

Duck³

2013

IMA Journal of Management Mathematics

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We present a quantitative method to find jointly optimal strategies for an industry regulator and a firm, who operate under exogenous uncertainty. The firm controls its operating policy in order to maximize its expected future profits, whilst taking account of regulatory fines. The regulator aims to control the probability of the firm terminating production, by imposing a closure fine which is as low as possible, while achieving the required reduction in probability. Our method determines the level of fine which establishes a Nash equilibrium in these nonzero-sum games, under uncertainty.

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Noise in hysteretic systems and stochastic processes on graphs

Abstract: It is shown that the theory of stochastic diffusion processes on graphs is a natural tool for the analysis of noise in hysteretic systems. In particular, by using this theory, analytical expressions for stationary characteristics of random outputs of some hysteretic systems are derived.

Cited by 16 publications

References 15 publications

On the constructions of the skew Brownian motion

On the constructions of the skew Brownian motion

Dynamic approximation of rectangular loops and aftereffect

Optimal regulatory control of early contract termination

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