Random Operators and Stochastic Equations

Published by De Gruyter

Volume 30 Issue 1

Issue of Random Operators and Stochastic Equations

Contents
Journal Overview

Publicly Available March 1, 2022

Frontmatter

Page range: i-iv

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January 6, 2022

Multivalued and random version of Perov fixed point theorem in generalized gauge spaces

A. Laadjel, Juan J. Nieto, Abdelghani Ouahab, Rosana Rodríguez-López

Page range: 1-19

Abstract

In this paper, we present some random fixed point theorems in complete gauge spaces. We establish then a multivalued version of a Perov–Gheorghiu’s fixed point theorem in generalized gauge spaces. Finally, some examples are given to illustrate the results.

January 6, 2022

Deplay BSDEs driven by fractional Brownian motion

Sadibou Aidara, Ibrahima Sane

Page range: 21-31

Abstract

This paper deals with a class of deplay backward stochastic differential equations driven by fractional Brownian motion (with Hurst parameter H greater than 1 2 {\frac{1}{2}} ). In this type of equation, a generator at time t can depend not only on the present but also the past solutions. We essentially establish existence and uniqueness of a solution in the case of Lipschitz coefficients and non-Lipschitz coefficients. The stochastic integral used throughout this paper is the divergence-type integral.

January 23, 2022

Solving equations with semimartingale noise

Jonathan Gutierrez-Pavón, Carlos G. Pacheco

Page range: 33-38

Abstract

In this work we focus on a method for solving equations with a coefficient formally given in terms of the derivative of a continuous semimartingale. This generalizes the case of coefficients being the white noise. The idea for solving the equation is to find explicitly the inverse of the ill-posed differential operator, which boils down to finding the associated Green kernel. To find the kernel we give explicitly two homogeneous solutions in terms of the so-called Dolean–Dade exponential. The general idea to define rigorously differential operators lies on dealing with them through bilinear forms. We give several examples with explicit calculations.

March 26, 2022

The main probability G-density of the theory of non-Hermitian random matrices, VICTORIA transform, RESPECT and REFORM methods

Vyacheslav L. Girko

Page range: 39-69

Abstract

The main probability G -density of the global law for random matrices whose entries are independent is founded.

March 26, 2022

The G-pencil law under G-Lindeberg condition. The canonical equation K_₉₈ and G-logarithmic law

Vyacheslav L. Girko, B. V. Shevchuk, L. D. Shevchuk

Page range: 71-84

Abstract

The examples of the pencil law for two random matrices whose pairs of entries are independent are considered.

About this journal

Objective
Random Operators and Stochastic Equations is devoted to the theory of random operators and stochastic analysis. Contributions on theoretical aspects, as well as on physical and technical applications are considered for publication.

Topics

general theory of linear random operators,
theory of random matrices, chaos in classical and quantum mechanics,
stochastic differential equations,
Brownian motion theory,
neural networks theory,
regression analysis,
multivariate statistical analysis,
systems of linear algebraic equations with random coefficients,
spectral decomposition of the solutions of operator stochastic equations,
pattern recognition,
discriminant analysi
stochastic control theory.

Article formats
Research articles

Information on submission process

Volume 30 Issue 1

Issue of Random Operators and Stochastic Equations

Frontmatter

Multivalued and random version of Perov fixed point theorem in generalized gauge spaces

Abstract

Deplay BSDEs driven by fractional Brownian motion

Abstract

Solving equations with semimartingale noise

Abstract

The main probability G-density of the theory of non-Hermitian random matrices, VICTORIA transform, RESPECT and REFORM methods

Abstract

The G-pencil law under G-Lindeberg condition. The canonical equation K_98 and G-logarithmic law

Abstract

The G-pencil law under G-Lindeberg condition. The canonical equation K_₉₈ and G-logarithmic law