Properties of $\varphi$-sub-Gaussian stochastic processes related to the heat equation with random initial conditions

  • O. M. Hopkalo Taras Shevchenko National University of Kyiv
  • L. M. Sakhno Taras Shevchenko National University of Kyiv
  • O. I. Vasylyk Taras Shevchenko National University of Kyiv https://orcid.org/0000-0002-0880-3751

Abstract

In this paper, there are studied sample paths properties of stochastic processes representing solutions (in $L_2(\Omega)$ sense) of the heat equation with random initial conditions given by $\varphi$-sub-Gaussian stationary processes. The main results are the bounds for the distributions of the suprema for such stochastic processes considered over bounded and unbounded domains.

Key words: φ-sub-Gaussian processes, heat equation, random initial condition, distribution of supremum.

Pages of the article in the issue: 17 - 24

Language of the article: English

References

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How to Cite
Hopkalo, O. M., Sakhno, L. M., & Vasylyk, O. I. (1). Properties of $\varphi$-sub-Gaussian stochastic processes related to the heat equation with random initial conditions. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, (1-2), 17-24. https://doi.org/10.17721/1812-5409.2020/1-2.2
Section
Algebra, Geometry and Probability Theory