Abstract
In this paper, there are studied sample paths properties of stochastic processes representing solutions (in L_2(Ω) sense) to the linear Korteweg–de Vries equation (called also the Airy equation) with random initial conditions given by φ-sub-Gaussian stationary processes. The main results are the bounds for the distributions of the suprema for such stochastic processes considered over bounded domains. Also, there are presented some examples to illustrate the results of the study.
Publisher
Taras Shevchenko National University of Kyiv
Subject
Medical Assisting and Transcription,Medical Terminology
Reference18 articles.
1. Gaussian Limiting Behavior of the Rescaled Solution to the Linear Korteweg de Vries Equation with Random Initial Conditions;BEGHIN;J Stat Phys Vol 99 Iss 3/4,2000
2. On the Solutions of Linear Odd-Order Heat-Type Equations with Random Initial Conditions;BEGHIN;J Stat Phys Vol 127 Iss 4,2007
3. GIULIANO ANTONINI R., KOZACHENKO YU., NIKITINA T. (2003) Space of φ-sub-Gaussian random variables. Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5). Vol. 27. P. 92-124.
4. BULDYGIN, V. V., KOZACHENKO, YU. V. (2000) Metric Characterization of Random Variables and Random Processes. American Mathematical Society, Providence, RI. 257 p.
5. Investigation of sample paths properties for some classes of φ-sub-Gaussian stochastic processes;HOPKALO;Modern Stoch Theory Appl Vol 8 Iss 1,2021