G. P. Samorodnitsky, M. Grigoriu, “Characteristic function for the stationary state of a one-dimensional dynamical system with Lévy noise”, TMF, 150:3 (2007), 391–408; Theoret. and Math. Phys., 150:3 (2007), 332

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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 150, Number 3, Pages 391–408
DOI: https://doi.org/10.4213/tmf5986 (Mi tmf5986)

This article is cited in 12 scientific papers (total in 12 papers)

Characteristic function for the stationary state of a one-dimensional dynamical system with Lévy noise

G. P. Samorodnitsky, M. Grigoriu

Cornell University

Full-text PDF (582 kB) Citations (12)

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DOI: https://doi.org/10.4213/tmf5986

Abstract: We develop a practical method for calculating the characteristic function of diffusion processes driven by Lévy white noise. The method is based on the Itô formula for semimartingales, a differential equation developed for the characteristic function of diffusion processes driven by Poisson white noise with jumps that may not have finite moments, and on approximate representations of the Lévy white noise process. Numerical results show that the proposed method is very accurate and is consistent with previous theoretical findings.

Keywords: diffusion with jumps, Lévy white noise, characteristic function, stationary solution, Itô formula.

Received: 14.04.2006

English version:
Theoretical and Mathematical Physics, 2007, Volume 150, Issue 3, Pages 332–346
DOI: https://doi.org/10.1007/s11232-007-0025-0

Bibliographic databases:

Language: Russian

Citation: G. P. Samorodnitsky, M. Grigoriu, “Characteristic function for the stationary state of a one-dimensional dynamical system with Lévy noise”, TMF, 150:3 (2007), 391–408; Theoret. and Math. Phys., 150:3 (2007), 332–346

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https://www.mathnet.ru/eng/tmf5986

https://doi.org/10.4213/tmf5986

https://www.mathnet.ru/eng/tmf/v150/i3/p391

This publication is cited in the following 12 articles:

Capala K., Dybiec B., “Multimodal Stationary States in Symmetric Single-Well Potentials Driven By Cauchy Noise”, J. Stat. Mech.-Theory Exp., 2019, 033206
Ghusinga Kh.R., Lamperski A., Singh A., “Estimating Stationary Characteristic Functions of Stochastic Systems Via Semidefinite Programming”, 2018 European Control Conference (Ecc), IEEE, 2018, 2720–2725
Alotta G. Di Paola M., “Probabilistic Characterization of Nonlinear Systems Under Alpha-Stable White Noise Via Complex Fractional Moments”, Physica A, 420 (2015), 265–276
Szczepaniec K., Dybiec B., “Stationary States in Two-Dimensional Systems Driven By Bivariate Levy Noises”, Phys. Rev. E, 90:3 (2014), 032128
Gioacchino Alotta, Mario Di Paola, ICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014, 2014, 1
Cottone G., “Statistics of nonlinear stochastic dynamical systems under Levy noises by a convolution quadrature approach”, Journal of Physics A-Mathematical and Theoretical, 44:18 (2011), 185001
Pavlyukevich I., Dybiec B., Chechkin A.V., Sokolov I.M., “Levy ratchet in a weak noise limit: Theory and simulation”, The European Physical Journal Special Topics, 191:1 (2010), 223–237
Dybiec B., Sokolov I.M., Chechkin A.V., “Stationary states in single-well potentials under symmetric Levy noises”, J Stat Mech Theory Exp, 2010, P07008
Potrykus A., Adhikari S., “Dynamical response of damped structural systems driven by jump processes”, Probabilistic Engineering Mechanics, 25:3 (2010), 305–314
Grigoriu M., “Numerical solution of stochastic differential equations with Poisson and Lévy white noise”, Phys. Rev. E, 80:2 (2009), 026704, 9 pp.
del-Castillo-Negrete D., Gonchar V.Yu., Chechkin A.V., “Fluctuation-driven directed transport in the presence of Levy flights”, Physica A: Statistical Mechanics and its Applications, 387:27 (2008), 6693–6704
Jumarie G., “Generalized Fokker-Planck equation for a class of stochastic dynamical systems driven by additive Gaussian and Poissonian fractional white noises of order alpha”, Central European Journal of Physics, 6:3 (2008), 737–753

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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