Related papers: Stochastic Volterra equations of nonscalar type in…
We investigate the quality of space approximation of a class of stochastic integral equations of convolution type with Gaussian noise. Such equations arise, for example, when considering mild solutions of stochastic fractional order partial…
We present two integrable discretisations of a general differential-difference bicomponent Volterra system. The results are obtained by discretising directly the corresponding Hirota bilinear equations in two different ways. Multisoliton…
We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let…
We construct infinitely many H\"older continuous, global-in-time, and stationary solutions to the stochastic Euler equations and the hypodissipative Navier-Stokes equations, taking values in the space $C(\mathbb{R};C^{\vartheta})$. For the…
In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the…
In this paper, we introduce Volterra evolution algebras which are evolution algebras whose structural matrices are described by skew symmetric matrices. A main result of the present paper gives a connection between such kind of algebras…
In this paper we characterise the Lp stability of perturbed linear Volterra integrodifferential convolution equations. Additionally we provide a framework which points to necessary and sufficient conditions on the forcing function that…
Optimal control of interacting particles governed by stochastic evolution equations in Hilbert spaces is an open area of research. Such systems naturally arise in formulations where each particle is modeled by stochastic partial…
We introduce a local non-determinism condition for Volterra It\^{o} processes that captures smoothing properties of possibly degenerate noise. By combining the stochastic sewing lemma with one-step Euler approximations, we first prove the…
The solution of integro-differential equations have a major role in the fields of science and engineering. Different approaches both numerical and analytic are used to solve these type of equations. In this paper, the solution of fuzzy…
The construction of stochastic solutions for nonlinear partial differential equations is a powerful method to obtain new exact results and to develop efficient numerical algorithms, in particular when domain decomposition techniques are…
In the study of concavity properties of positive solutions to nonlinear elliptic partial differential equations the diffusion and the nonlinearity are typically independent of the space variable. In this paper we obtain new results aiming…
Consider the stochastic evolution equation in a separable Hilbert space with a nice multiplicative noise and a locally Dini continuous drift. We prove that for any initial data the equation has a unique (possibly explosive) mild solution.…
The holographic principle suggests that the Hilbert space of quantum gravity is locally finite-dimensional. Motivated by this point-of-view, and its application to the observable Universe, we introduce a set of numerical and conceptual…
The numerical method for solution of the weakly regular scalar Volterra integral equation of the 1st kind is proposed. The kernels of such equations have jump discontinuities on the continuous curves which starts at the origin. The…
This paper presents stochastic virtual element methods for propagating uncertainty in linear elastic stochastic problems. We first derive stochastic virtual element equations for 2D and 3D linear elastic problems that may involve…
We extend existence and uniqueness results of [4] for nonlinear integro-differential equations of Volterra type between real locally complete vector spaces
The Duffing oscillator is a paradigm of bistable oscillatory motion in physics, engineering, and biology. Time series of such oscillations are often observed experimentally in a nonlinear system excited by a spontaneously fluctuating force.…
In this work we study the long time behavior of nonlinear stochastic functional-differential equations of neutral type in Hilbert spaces with non-Lipschitz nonlinearities. We establish the existence of invariant measures in the shift spaces…
Under mild conditions, it is possible to obtain, from almost purely measure-theoretic considerations and without any specific reference to stochastic processes, a change-of-measures result, resembling the usual Radon-Nikod\'ym change of…