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Mean exit time for a chain of N = 2,3,4 oscillators

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Abstract

An asymptotic formula is obtained for an average breaking time for a chain of harmonic oscillators consisted of N = 2,3,4 particles with nearest-neighbor interaction and a random external force.

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References

  1. A. D. Ventsel’ and M. L Freidlin, Fluctuation in Dynamic Systems under the Action of Small Random perturbations (Nauka, Moscow, 1979) [in Russian].

    Google Scholar 

  2. M. Gitterman, The Noisy Oscillator (World Sei. Publ. Co. Re. Ltd., Singapore, 2005).

    MATH  Google Scholar 

  3. A. A. Lykov, V. A. Malyshev, and S. A Muzychka, “Linear Hamiltonian Systems with Tiny Random Action,” Teor. Veroyatn i Primenen. 57(4), 794 (2012).

    Article  Google Scholar 

  4. I. I. Gikhman and A. V. Skorokhod, Theory of Random, Processes. Vol. 1 (Nauka, Moscow, 1971) [in Russian].

    Google Scholar 

  5. A. N. Shiryaev, “Martingale Methods if Problems of Boundary Crossing by Brownian Motion,” in Modern Problems of Mathematics, Issue 8 (V. A. Steklov Math. Inst, of RAS, Moscow, 2007), pp. 3–78.

    Google Scholar 

  6. A. V. Bulinskii and A. N. Shiryaev, Theory of Random Processes (Fizmatlit, Moscow, 2004) [in Russian].

    Google Scholar 

  7. S. N. Ethier and T. G. Kurtz, Markov Processes, Characterization and Convergence (John Wiley and Sons, Hoboken, N.J., 1986)

    Book  MATH  Google Scholar 

  8. A. D. Ventsel’, The Course of the Theory of Random Processes (Nauka, Fizmatlit, Moscow, 1996) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    S. A. Muzychka

Authors
  1. S. A. Muzychka
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Additional information

Original Russian Text © S.A. Muzychka, 2013, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2013, Vol. 67, No. 4, pp. 46–51.

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Muzychka, S.A. Mean exit time for a chain of N = 2,3,4 oscillators. Moscow Univ. Math. Bull. 68, 206–210 (2013). https://doi.org/10.3103/S0027132213040086

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  • DOI: https://doi.org/10.3103/S0027132213040086

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