Related papers: Second Moment Boundedness of Linear Stochastic Del…
We derive two-sided bounds for moments of random multilinear forms (random chaoses) with nonnegative coeficients generated by independent nonnegative random variables $X_i$ which satisfy the following condition on the growth of moments:…
Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…
In this paper we obtain an algorithm towards solving the two-dimensional moment problem. This algorithm gives the necessary and sufficient conditions for the solvability of the moment problem. It is shown that all solutions of the moment…
We unify and extend the semigroup and the PDE approaches to stochastic maximal regularity of time-dependent semilinear parabolic problems with noise given by a cylindrical Brownian motion. We treat random coefficients that are only…
In this paper we study the reachability problem for discrete-time nonlinear stochastic systems. Our goal is to present a unified framework for calculating the probabilistic reachable set of discrete-time systems in the presence of both…
This paper investigates the local boundedness of weak solutions to a direction-dependent double-phase nonlocal elliptic equation. By employing refined energy estimates and De Giorgi-type techniques, we establish the local boundedness of…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
We obtain uniqueness and existence of a solution $u$ to the following second-order stochastic partial differential equation (SPDE) : \begin{align} \label{abs eqn} du= \left( \bar a^{ij}(\omega,t)u_{x^ix^j}+ f \right)dt + g^k dw^k_t, \quad t…
The Boltzmann equation, a fundamental equation in kinetic theory, serves as a bridge between microscopic particle dynamics and macroscopic continuum mechanics. However, deriving closed macroscopic moment systems from the Boltzmann equation…
In this paper, the existence conditions of nonuniform mean-square exponential dichotomy (NMS-ED) for a linear stochastic differential equation (SDE) are established. The difference of the conditions for the existence of a nonuniform…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…
We propose a mathematical methodology to derive a stochastic parameterization of bulk warm cloud micro-physics properties. Unlike previous bulk parameterizations, the stochastic parameterization does not assume any particular droplet size…
This paper studies the stability properties of stochastic differential equations subject to persistent noise (including the case of additive noise), which is noise that is present even at the equilibria of the underlying differential…
In this work two-point boundary value problem for one class of second order ordinary differential equations with variable coefficients is solved.
We restrict our attention to space-time point pattern data for which we have a single realisation within a finite region. Second-order characteristics are used to analyse the spatio-temporal structure of the underlying point process. In…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
We consider nonlinear parabolic stochastic PDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish existence, uniqueness and moment…
For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…
We present an efficient finite difference method for the approximation of second derivatives, with respect to system parameters, of expectations for a class of discrete stochastic chemical reaction networks. The method uses a coupling of…