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

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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.

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References

  1. M. Grigoriu, Stochastic Calculus: Applications in Science and Engineering, Birkhäuser, Boston (2002).

    MATH  Google Scholar 

  2. M. Grigoriu, Probab. Eng. Mech., 19, 449–461 (2004).

    Article  Google Scholar 

  3. A. V. Chechkin and V. Yu. Gonchar, JETP, 91, 635–651 (2000).

    Article  ADS  Google Scholar 

  4. V. Yu. Gonchar, L. V. Tanatarov, and A. V. Chechkin, Theor. Math. Phys., 131, 582–594 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  5. G. Samorodnitsky and M. Grigoriu, Stochastic Process. Appl., 105, No. 3, 69–97 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  6. T. G. Kurtz and P. Protter, Ann. Probab., 19, 1035–1070 (1991).

    MATH  MathSciNet  Google Scholar 

  7. M. Grigoriu, Applied Non-Gaussian Processes: Examples, Theory, Simulation, Linear Random Vibration, and MATLAB Solutions, Prentice-Hall, Englewoods Cliffs, N. J. (1995).

    MATH  Google Scholar 

  8. B. V. Gnedenko, Course of Probability Theory [in Russian], Nauka, Moscow (1969); English transl.: Theory of Probability (6th ed.), Gordon and Breach, Newark, N. J. (1997).

    Google Scholar 

  9. G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman and Hall, New York (1994).

    MATH  Google Scholar 

  10. P. Protter, Stochastic Integration and Differential Equations (Appl. Math. N. Y., Vol. 21), Springer, Berlin (1990).

    MATH  Google Scholar 

  11. S. Asmussen and J. Rosiński, J. Appl. Probab., 38, 482–493 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  12. N. Fournier and S. Méléard, Bernoulli, 8, 537–558 (2002).

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Cornell University, Ithaca, New York, USA

    G. Samorodnitsky & M. Grigoriu

Authors
  1. G. Samorodnitsky
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  2. M. Grigoriu
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 3, pp. 391–408, March, 2007.

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Samorodnitsky, G., Grigoriu, M. Characteristic function for the stationary state of a one-dimensional dynamical system with Lévy noise. Theor Math Phys 150, 332–346 (2007). https://doi.org/10.1007/s11232-007-0025-0

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  • DOI: https://doi.org/10.1007/s11232-007-0025-0

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