On stochastic space-time Paley-Wiener-Zygmund integral

Authors

DOI:

https://doi.org/10.31652/3041-1955-2024-01-02

Keywords:

stochastic integral, Paley-Wiener-Zygmund integral, random Winer process

Abstract

We consider one case of the stochastic integral of non-random function of many variables with respect to the random Winer process. We give definition of this integral and prove some it standard properties.

Author Biographies

  • Oleh Buhrii, Lviv University
    Doctor of Science in Physics and Mathematics, Professor, Department of Mathematical Statistics and Differential Equations
  • Nataliya Buhrii, Lviv Polytechnic National University
    Candidate of Science in Physics and Mathematics, Department of Mathematics
  • Vitaliy Vlasov, Lviv University
    Candidate of Science in Physics and Mathematics, Department of Mathematical Statistics and Differential Equations

References

Evans L. C. An introduction to Stochastic differential equations. Lecture Notes (VERSION 1.2). 2012. Department of Math., UC Berkeley. 139 p.

Paley R., Wiener N., Zygmund A. Notes on random functions. Mathematische Zeitschrift. 1933. Vol. 37, № 1. P. 647-668. https://doi.org/10.1007/BF01474606

Applebaum D. Levy processes and stochastic calculus. Cambridge: Cambridge University Press, 2009. 460 p. https://doi.org/10.1017/CBO9780511809781

Brezis H. Functional Analysis. Sobolev Spaces and Partial Differential Equations. New York, Dordrecht, Heidelberg, London: Springer, 2011. 599 p. https://doi.org/10.1007/978-0-387-70914-7

Leoni G. A first course in Sobolev spaces. Providence: American Mathematical Soc., 2017. 736 p. https://doi.org/10.1090/gsm/181

Гнєденко Б. В. Курс теорії ймовірностей. Київ: Видавничо-поліграфічний центр "Київський університет", 2010. 464 c.

Скороход А. В. Лекції з теорії випадкових процесів. Київ: Либідь, 1990. 168 c.

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Published

2024-06-20

Issue

Vol. 1 No. 1 (2024)

Section

Actual problems of mathematics

License

Copyright (c) 2024 Олег Бугрій, Наталія Бугрій, Віталій Власов (Автор)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

On stochastic space-time Paley-Wiener-Zygmund integral. (2024). Mathematics, Informatics, Physics: Science and Education, 1(1), 13-26. https://doi.org/10.31652/3041-1955-2024-01-02