相关论文: On the Admissibility of Linear Stochastic Volterra…

Two necessary and sufficient conditions for an operator to be semi-normal are revealed. For a Volterra integration operator the set where the operator and its adjoint are metrically equal is described.

We study linear-quadratic optimal control problems for Voterra systems, and problems that are linear-quadratic in the control but generally nonlinear in the state. In the case of linear-quadratic Volterra control, we obtain sharp necessary…

We discuss conditions ensuring the (strict) convergence of stochastic gradient algorithms.

In this paper stochastic Volterra equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties for stochastic convolutions are studied. Our main result provide sufficient…

In the present paper we introduce a notion of homotopy of two Volterra operators which is related to fixed points of such operators. It is establish a criterion when two Volterra operators are homotopic, as a consequence we obtain that the…

We study the almost sure convergence of randomly truncated stochastic algorithms. We present a new convergence theorem which extends the already known results by making vanish the classical condition on the noise terms. The aim of this work…

We develop a unified framework for constructing matrix approximations to the convolution operator of Volterra type defined by functions that are approximated using classical orthogonal polynomials on $[-1, 1]$. The numerically stable…

We consider a four-parametric $(a, b, \alpha, \beta)$ family of Volterra quadratic stochastic operators for a bisexual population (i.e., each organism of the population must belong either to the female sex or the male sex). We show that…

We define a stochastic variant of the proximal point algorithm in the general setting of nonlinear (separable) Hadamard spaces for approximating zeros of the mean of a stochastically perturbed monotone vector field and prove its convergence…

We consider a four-parameter family of non-Volterra operators defined on the two-dimensional simplex and show that, with one exception, each such operator has a unique fixed point. Depending on the parameters, we establish the type of this…

We consider $\ell$-Volterra quadratic stochastic operators defined on $(m-1)$-dimensional simplex, where $\ell\in\{0,1,...,m\}$. Under some conditions on coefficients of such operators we describe Lyapunov functions and apply them to obtain…

Reference [11] investigated the almost sure weak convergence of block-coordinate fixed point algorithms and discussed their applications to nonlinear analysis and optimization. This algorithmic framework features random sweeping rules to…

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a…

Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…

In this paper we propose new sufficient conditions for stability of solutions of systems of Volterra linear integral equations and systems of linear integro-differential Volterra equations. Solution stability conditions for systems of…

We propose stochastic splitting algorithms for solving large-scale composite inclusion problems involving monotone and linear operators. They activate at each iteration blocks of randomly selected resolvents of monotone operators and,…

In this paper stochastic Volterra equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties of stochastic convolutions are given. The paper provides a sufficient condition…

We compute the operator norm of real-quadratic polynomials of the Volterra operator. This is used to test whether the Crouzeix conjecture holds for the Volterra operator.

Many optimization algorithms$\unicode{x2013}$including gradient descent, proximal methods, and operator splitting techniques$\unicode{x2013}$can be formulated as fixed-point iterations (FPI) of continuous operators. When these operators are…

We establish spectral convergence results of approximations of unbounded non-selfadjoint linear operators with compact resolvents by operators that converge in generalized strong resolvent sense. The aim is to establish general assumptions…