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On Some Probabilistic Problems in the Theory of Quadratic Operators

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Nonlinearity with Disorder

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 67))

Abstract

A Central Limit Theorem and conditions which imply the ergodic principle are studied for quadratic process which are related to quadratic operators in the same way as Markov processes are related to linear operators.

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References

  1. Kesten H. Quadratic transformation: A model for population grouth I. Adv. Appl. Prob. 1970, v. 2, No 1, P. 1–82.

    Article  MATH  MathSciNet  Google Scholar 

  2. Jenks R.D. Quadratic differential systems for interactive population models. J. Diff. Equation, 1969, v. 5, No 3, P. 497–514.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  3. Sarymsakov T.A., Ganikhodzhaev N.N. Analytic methods in the theory of quadratic stochastic operators. Soviet Math. Dokl., 1989, v. 39, No 2, P. 369–373.

    MATH  MathSciNet  Google Scholar 

  4. Sarymsakov T.A., Ganikhodzhaev N.N. Analytic methods in the theory of quadratic stochastic operators. J. of Theoretical Prob. 1990, v. 3, No 1, P. 51–70.

    Article  MATH  MathSciNet  Google Scholar 

  5. Kolmogorov A.N. On analytic methods in the probability theory. Uspekhi Mat. Nauk 1938, No 5, P 5–51.

    MathSciNet  Google Scholar 

  6. Ganikhodzhaev N.N. On averaging of quadratic stochastic processes. Dokl. Acad. Nauk of Uzbek SSR, 1989, No 10, P. 7–9, (in Russian).

    MathSciNet  Google Scholar 

  7. Kimura M. Diffusion models in population genetics. J. Appl. Prob., 1969, v. 1, P. 177–232.

    Article  Google Scholar 

  8. Dobrushin R.L. Central Limit Theorem for non—stationary Markov chains. Teor. Veroyat. i Primenen. 1956, v. 1, No 1, P. 72–89, (in Russian).

    MATH  MathSciNet  Google Scholar 

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© 1992 Springer-Verlag Berlin Heidelberg

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Sarymsakov, T.A., Ganikhodzhaev, N.N. (1992). On Some Probabilistic Problems in the Theory of Quadratic Operators. In: Abdullaev, F., Bishop, A.R., Pnevmatikos, S. (eds) Nonlinearity with Disorder. Springer Proceedings in Physics, vol 67. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84774-5_15

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  • DOI: https://doi.org/10.1007/978-3-642-84774-5_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-84776-9

  • Online ISBN: 978-3-642-84774-5

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