Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditions
Open Access
- 17 December 2019
- journal article
- research article
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 7 (1), 79-96
- https://doi.org/10.15559/19-vmsta146
Abstract
Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditions, Authors: Yuriy Kozachenko, Enzo Orsingher, Lyudmyla Sakhno, Olga Vasylyk , In the paper we consider higher-order partial differential equations from the class of linear dispersive equations. We investigate solutions to these equations subject to random initial conditions given by harmonizable φ-sub-Gaussian processes. The main results are the bounds for the distributions of the suprema for solutions. We present the examples of processes for which the assumptions of the general result are verified and bounds are written in the explicit form. The main result is also specified for the case of Gaussian initial condition.Keywords
This publication has 11 references indexed in Scilit:
- Estimates for Functionals of Solutions to Higher-Order Heat-Type Equations with Random Initial ConditionsJournal of Statistical Physics, 2018
- Whittaker–Kotel'nikov–Shannon approximation of φ-sub-Gaussian random processesJournal of Mathematical Analysis and Applications, 2016
- Probabilistic representation of fundamental solutions to $\frac{\partial u}{\partial t} = κ_m \frac{\partial^m u}{\partial x^m}$Electronic Communications in Probability, 2012
- On the Solutions of Linear Odd-Order Heat-Type Equations with Random Initial ConditionsJournal of Statistical Physics, 2007
- Nonlinear Dispersive EquationsCBMS Regional Conference Series in Mathematics, 2006
- Simulation of Gaussian stochastic processesRandom Operators and Stochastic Equations, 2003
- Covariance analysis and associated spectra for classes of nonstationary processesJournal of Statistical Planning and Inference, 2002
- Gaussian Limiting Behavior of the Rescaled Solution to the Linear Korteweg–de Vries Equation with Random Initial ConditionsJournal of Statistical Physics, 2000
- Boundary-Value problems with random initial conditions and functional series from subφ (Ω). IUkrainian Mathematical Journal, 1998
- 10 Harmonizable, Cramér, and Karhunen classes of processesPublished by Elsevier BV ,1985