Related papers: Nonconvolution nonlinear integral Volterra equatio…
Let $A$ be a densely defined closed, linear $\omega$-sectorial operator of angle $\theta\in [0,\frac{\pi}{2})$ on a Banach space $X$ for some $\omega\in\mathbb R$. We give an explicit representation (in terms of some special functions) and…
We introduce affine Volterra processes, defined as solutions of certain stochastic convolution equations with affine coefficients. Classical affine diffusions constitute a special case, but affine Volterra processes are neither…
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 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 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 consider an integral equation in the plane, in which the leading operator is of convolution type, and we prove that monotone (or stable) solutions are necessarily one-dimensional.
In this paper, we study existence of solutions to a conformally invariant integral equation involving Poisson-type kernels. Such integral equation has a stronger non-local feature and is not the dual of any PDE. We obtain the existence of…
In this paper, we study the existence and uniqueness of solutions for several classes of stochastic evolution equations with non-Lipschitz coefficients, that is, backward stochastic evolution equations, stochastic Volterra type evolution…
Equations of Hammerstein type cover large variety of areas and are of much interest to a wide audience due to the fact that they have applications in numerous areas. Suitable conditions are imposed to obtain a strong convergence result for…
This paper concerns the asymptotic behaviour of solutions of a linear convolution Volterra summation equation with an unbounded forcing term. In particular, we suppose the kernel is summable and ascribe growth bounds to the exogenous…
The class of nonlinear integral equations on the positive half-line with a monotone operator of Hammerstein type is studied. With various partial representations of the corresponding kernel and nonlinearity, this class of equations has…
A new expression for solving homogeneous linear ODEs based on a generalization of the Volterra composition was recently introduced. In this work, we extend such an expression, showing that it corresponds to inverting an infinite matrix.…
We provide a new existence result for abstract nonlinear operator systems in normed spaces, by means of topological methods. The solution is located within the product of annular regions and conical shells. The theoretical result possesses…
The inverse nodal problem for Dirac differential operator perturbated by a Volterra integral operator is studied. We prove that dense subset of the nodal points determines the coefficients of differential and integral part of the operator.…
We establish Burkholder-Davis-Gundy-type inequalities for stochastic Volterra integrals with a completely monotone convolution kernel, which may exhibit singular behaviour at the origin. When the supremum is taken over a finite interval,…
Sufficient conditions for existence and uniqueness of the solution of the Volterra integral equations of the first kind with piecewise continuous kernels are derived in framework of Sobolev-Schwartz distribution theory. The asymptotic…
Modeling nonlinear systems with Volterra series is challenging because the number of kernel coefficients grows exponentially with the model order. This work introduces Bayesian Tensor Network Volterra kernel machines (BTN-V), extending the…
This paper deals with inverse problems subject to imprecise or vague information of some involved data by means of interval-valued functions. To provide interval solutions to the inverse problems we have adopted a perturbed collage-based…
We consider convolution integral equations on a finite interval with a real-valued kernel of even parity, a problem equivalent to finding a Wiener-Hopf factorisation of a notoriously difficult class of $2\times 2$ matrices. The kernel…
A discrepancy principle for solving nonlinear equations with monotone operators given noisy data is formulated. The existence and uniqueness of the corresponding regularization parameter $a(\delta)$ is proved. Convergence of the solution…