Related papers: Pathwise mild solutions for superlinear stochastic…

We obtain Calder\'on-Zygmund type estimates for parabolic equations with Orlicz growth, where nonlinearities involved in the equations may be discontinuous for the space and time variables. In addition, we consider parabolic systems with…

A new explicit stochastic scheme of order 1 is proposed for solving commutative stochastic differential equations (SDEs) with non-globally Lipschitz continuous coefficients. The proposed method is a semi-tamed version of Milstein scheme to…

This paper presents a direct method to obtain the deterministic and stochastic contribution of the sum of two independent sets of stochastic processes, one of which is composed by Ornstein-Uhlenbeck processes and the other being a general…

We introduce a flexible and tractable infinite-dimensional stochastic volatility model. More specifically, we consider a Hilbert space valued Ornstein-Uhlenbeck-type process, whose instantaneous covariance is given by a pure-jump stochastic…

In this paper, we establish the well-posedness and optimal trajectory regularity for the solution of stochastic evolution equations with generalized Lipschitz-type coefficients driven by general multiplicative noises. To ensure the…

Large-time behaviour of solutions to stochastic evolution equations driven by two-sided regular Volterra processes is studied. The solution is understood in the mild sense and takes values in a separable Hilbert space. Sufficient conditions…

We study coupled non-linear parabolic equations for a fluid described by a material density and a temperature, both functions of space and time. In one dimension, we find some stationary solutions corresponding to fixing the temperature on…

We prove existence of variational solutions for a class of nonlocal evolution equations whose prototype is the double phase equation \begin{align*} \partial_t u &+ \text{P.V.}\int_{\mathbb{R}^N}…

Combining fractional calculus and the Rough Path Theory we study the existence and uniqueness of mild solutions to evolutions equations driven by a H\"older continuous function with H\"older exponent in $(1/3,1/2)$. Our stochastic integral…

The main purpose of this paper is to give an upper bound of Hausdorff dimension of random attractors for a stochastic delayed parabolic equation in Banach spaces. The estimation of dimensions of random attractors are obtained by combining…

We derive a Gronwall type inequality for mild solutions of non-autonomous parabolic rough partial differential equations (RPDEs). This inequality together with an analysis of the Cameron-Martin space associated to the noise, allows us to…

Motivated by the work of T.E. Govindan in [5,8,9], this paper is concerned with a more general semilinear stochastic evolution equation. The difference between the equations considered in this paper and the previous one is that it makes…

We prove a modification to the classical maximal inequality for stochastic convolutions in 2-smooth Banach spaces using the factorization method. This permits to study semilinear stochastic partial differential equations with unbounded…

We prove the existence of statistically stationary solutions to the Schr\"odinger map equation on a one-dimensional domain, with null Neumann boundary conditions. We deal directly with the equation in its real-valued formulation, without…

Moving boundary problems allow to model systems with phase transition at an inner boundary. Driven by problems in economics and finance, in particular modeling of limit order books, we consider a stochastic and non-linear extension of the…

We present strongly convergent explicit and semi-implicit adaptive numerical schemes for systems of stiff stochastic differential equations (SDEs) where both the drift and diffusion are non-globally Lipschitz continuous. This stiffness may…

We combine earlier investigations of linear systems with L\'{e}vy fluctuations [Physica {\bf 113A}, 203, (1982)] with recent discussions of L\'{e}vy flights in external force fields [Phys.Rev. {\bf E 59},2736, (1999)]. We give a complete…

We construct space-time stationary solutions of the 1D Burgers equation with random forcing in the absence of periodicity or any other compactness assumptions. More precisely, for the forcing given by a homogeneous Poissonian point field in…

In this article, we consider mild solutions to a class of impulsive fractional evolution equations of order $0<\alpha<1$. After analyzing analytic results reported in the literature using Mittag-Leffer function, $\alpha$-resolvent operator…

This paper deals with the existence and uniqueness of ($\mu$-pseudo) almost periodic mild solution to some evolution equations with Stepanov ($\mu$-pseudo) almost periodic coefficients, in both determinist and stochastic cases. After…