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TMF, 2007, Volume 150, Number 3, Pages 391–408 (Mi tmf5986)  

This article is cited in 9 scientific papers (total in 9 papers)

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

G. P. Samorodnitsky, M. Grigoriu

Cornell University

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

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

Full text: PDF file (582 kB)
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English version:
Theoretical and Mathematical Physics, 2007, 150:3, 332–346

Bibliographic databases:

Received: 14.04.2006

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

    This publication is cited in the following articles:
    1. 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  crossref  adsnasa  isi  scopus
    2. 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  crossref  adsnasa  isi  scopus
    3. Grigoriu M., “Numerical solution of stochastic differential equations with Poisson and Lévy white noise”, Phys. Rev. E, 80:2 (2009), 026704, 9 pp.  crossref  adsnasa  isi  scopus
    4. 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  crossref  mathscinet  adsnasa  isi  elib  scopus
    5. 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  crossref  isi  scopus
    6. Potrykus A., Adhikari S., “Dynamical response of damped structural systems driven by jump processes”, Probabilistic Engineering Mechanics, 25:3 (2010), 305–314  crossref  mathscinet  isi  elib  scopus
    7. 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  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. Szczepaniec K., Dybiec B., “Stationary States in Two-Dimensional Systems Driven By Bivariate Levy Noises”, Phys. Rev. E, 90:3 (2014), 032128  crossref  adsnasa  isi  scopus
    9. 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  crossref  mathscinet  adsnasa  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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