Skip to main content
Log in

Unbounded probability theory and multistep relaxation processes, II

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

This paper elucidates the relationship between the paper [1] and the standard approach in probability theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. V. P. Maslov, “Unbounded Probability Theory and Multistep Relaxation Processes,” Math. Notes 93(3), 451–459 (2013).

    Article  Google Scholar 

  2. A. I. Mal’tsev, Algebraic Systems (Nauka, Moscow, 1970) [in Russian].

    MATH  Google Scholar 

  3. V. P. Maslov and V. V. V’yugin, “Variational problems for additive loss functions and Kolmogorov complexity,” Dokl. Ross. Akad. Nauk 390(5), 595–598 (2003) [Russian Acad. Sci. Dokl. Math. 67 (3), 404–407 (2003)].

    MathSciNet  Google Scholar 

  4. V. V. V’yugin and V. P. Maslov, “Extremal Relations between Additive Loss Functions and the Kolmogorov Complexity,” Problemy Peredachi Informatsii 39(4) 71–87 (2003) [Problems Inform. Transmission 39 (4) 380–394 (2003)].

    MathSciNet  Google Scholar 

  5. V. V. V’yugin and V. P. Maslov, “Concentration Theorems for Entropy and Free Energy,” Problemy Peredachi Informatsii 41(2) 72–88 (2005) [Problems Inform. Transmission 41 (2) 134–149 (2005)].

    MathSciNet  Google Scholar 

  6. L. D. Landau and E. M. Lifshits, Statistical Physics (Nauka, Moscow, 1964) [in Russian].

    Google Scholar 

  7. V. P. Maslov and A. S. Chernyi, “On the maximization and minimization entropy in various disciplines,” Teor. Veroyatnost. i Primenen. 48(3), 466–486 (2003) [Theory Probab. Appl. 48 (3), 447–464 (2003)].

    Article  MathSciNet  Google Scholar 

  8. V. P. Maslov, “Integral Equations and Phase Transitions in Stochastic Games,” Teor. Veroyatnost. i Primenen. 48(2), 403–412 (2003) [Theory Probab. Appl. 48 (2), 359–367 (2004)].

    Article  Google Scholar 

  9. V. P. Maslov, “Quantum Statistics Methods from the Viewpoint of Probability Theory, Teor. Veroyatnost. i Primenen. 47(4), 686–709 (2002) [Theory Probab. Appl. 47 (4), 665–683 (2003)].

    Article  Google Scholar 

  10. A. N. Shiryaev, Foundations of Stochastic Financial Mathematics (FAZIS, Moscow, 1998), Vols. 1, 2 [in Russian].

    Google Scholar 

  11. A. N. Shiryaev, Probability, Vol. 1: Elementary Probability Theory. Mathematical Foundations. Limit Theorems (MCCME, Moscow, 2004) [in Russian].

    Google Scholar 

  12. V. P. Maslov and T. V. Maslova, “Unbounded probability theory and its applications”, Teor. Veroyatnost. Primenen. 57(3), 471–498 (2012).

    Article  MathSciNet  Google Scholar 

  13. E. T. Jaynes, Papers on Probability, Statistics, and Statistical Physics (Dordrecht, Reidel, 1984).

    Google Scholar 

  14. Y. Miyahara “Geometric Lévy process pricing model,” Trudy Mat. Inst. Steklov 237, 185–200 (2002) [Proc. Steklov Inst. Math. 237, 176–191 (2002)].

    MathSciNet  Google Scholar 

  15. H. Föllmer and A. Schied, Stochastic Finance: An Introduction in Discrete Time (de Gruyter, Berlin, 2002).

    Google Scholar 

  16. V. P. Maslov, “Econophysics and Quantum Statistics, Mat. Zametki 72(6), 883–891 (2002) [Math. Notes 72 (5–6), 811–818 (2002)].

    Article  Google Scholar 

  17. A. M. Vershik, “Statistical mechanics of combinatorial partitions and their limit shapes,” Funktsional. Anal. i Prilozhen. 30(2), 19–39 (1996) [Functional Anal. Appl. 30 (2), 90–105 (1996)].

    Article  MathSciNet  Google Scholar 

  18. V. P. Maslov, “A homogeneous gas mixture,” Teoret. Mat. Fiz. 168(2), 358–368 (2011) [Theoret. and Math. Phys. 168 (2), 1165–1174 (2002)].

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. P. Maslov.

Additional information

The article was submitted by the author for the English version of the journal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maslov, V.P. Unbounded probability theory and multistep relaxation processes, II. Math Notes 93, 881–889 (2013). https://doi.org/10.1134/S000143461305026X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S000143461305026X

Keywords

Navigation