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Problem of large deviations for Markov random evolutions with independent increments in the scheme of asymptotically small diffusion

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The problem of large deviations for random evolutions with independent increments is solved in the scheme of asymptotically small diffusion by passing to the limit in the nonlinear (exponential) generator of semigroups by using the solution of the problem of singular perturbation for a reducibly invertible operator.

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References

  1. 1.

    J. Feng and T. G. Kurtz, Large Deviation for Stochastic Processes, American Mathematical Society, Providence, RI (2006).

  2. 2.

    V. S. Korolyuk and N. Limnios, Stochastic Systems in Merging Phase Space, Word Scientific, Singapore (2005).

  3. 3.

    A. A. Mogulskii, “Large deviation for processes with independent increments,” Ann. Probab., 21, 202–215 (1993).

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Author information

Correspondence to V. S. Korolyuk.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 5, pp. 643–650, May, 2010.

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Korolyuk, V.S. Problem of large deviations for Markov random evolutions with independent increments in the scheme of asymptotically small diffusion. Ukr Math J 62, 739–747 (2010). https://doi.org/10.1007/s11253-010-0384-9

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Keywords

  • Brownian Motion
  • Singular Perturbation
  • Asymptotic Representation
  • Diffusion Approximation
  • Markov Jump