Related papers: The Local Time-Space Integral and Stochastic Diffe…
In this article we extend the exact simulation methods of Beskos et al. to the solutions of one-dimensional stochastic differential equations involving the local time of the unknown process at point zero. In order to perform the method we…
We consider a stochastic differential equation in a Hilbert space with time-dependent coefficients for which no general existence and uniqueness results are known. We prove, under suitable assumptions, existence and uniqueness of a measure…
We establish the existence and uniqueness of solutions to stochastic 2D Navier-Stokes equations in a time-dependent domain driven by Brownian motion. A martingale solution is constructed through domain transformation and appropriate…
Using a Tanaka representation of the local time for a class of superprocesses with dependent spatial motion, as well as sharp estimates from the theory of uniformly parabolic partial differential equations, the joint H\"older continuity in…
We present a detailed analysis of non-degenerate time-homogeneous It\^o-stochastic differential equations with low local regularity assumptions on the coefficients. In particular the drift coefficient may only satisfy a local integrability…
In this paper we study time-inhomogeneous versions of one-dimensional Stochastic Differential Equations (SDE) involving the Local Time of the unknown process on curves. After proving existence and uniqueness for these SDE under mild…
This article focuses on the space-time isogeometric method for a linear time dependent fourth order problem. Using an auxiliary variable, first the problem is split into a system of two second order differential equations and then the…
We study a class of stochastic time-fractional equations on $\mathbb{R}^d$ driven by a centered Gaussian noise, involving a Caputo time derivative of order $\beta>0$, a fractional (power) Laplacian of order $\alpha>0$, and a…
In this paper, we consider the local existence and uniqueness result for the inhomogeneous Prandtl equations in dimension two by energy method. First of all, for the homogeneous case, the local-in-time well-posedness theory of unsteady…
A space-time fully adaptive multiresolution method for evolutionary non-linear partial differential equations is presented introducing an improved local time-stepping method. The space discretisation is based on classical finite volumes,…
The rate of strong convergence is investigated for an approximation scheme for a class of stochastic differential equations driven by a time-changed Brownian motion, where the random time changes $(E_t)_{t\ge 0}$ considered include the…
We present a mathematical approach that simplifies the theoretical treatment of electromagnetic localization in random media and leads to closed form analytical solutions. Starting with the assumption that the dielectric permittivity of the…
We propose a numerical scheme to solve the time dependent linear Schr\"odinger equation. The discretization is carried out by combining a Runge-Kutta time-stepping scheme with a finite element discretization in space. Since the…
We consider the one-dimensional stochastic differential equation \begin{equation*} X_t = x_0 + L_t + \int_0^t \mu(X_s)ds, \quad t \geq 0, \end{equation*} where $\mu$ is a finite measure of Kato class $K_{\eta}$ with $\eta \in (0,\alpha-1]$…
We consider a general class of integro-differential evolution equations which includes the governing equation of the generalized grey Brownian motion and the time- and space-fractional heat equation. We present a general relation between…
Let $B_t$ be a one dimensional Brownian motion, and let $\alpha'$ denote the derivative of the intersection local time of $B_t$ as defined in Jay Rosen's work (see references). The object of this paper is to prove the following formula…
In the present paper, we give some examples of stochastic differential equations which have delicateness in the Markov and strong Markov properties, the uniqueness locally in time and globally in time, and initial conditions. Moreover, we…
We prove existence and uniqueness of solutions to Fokker--Planck equations associated to Markov operators multiplicatively perturbed by degenerate time-inhomogeneous coefficients. Precise conditions on the time-inhomogeneous coefficients…
In this paper we consider a class of time-dependent neutral stochastic functional differential equations with finite delay driven by a fractional Brownian motion in a Hilbert space. We prove an existence and uniqueness result for the mild…
Three concepts of local times for deterministic c{\`a}dl{\`a}g paths are developed and the corresponding pathwise Tanaka--Meyer formulae are provided. For semimartingales, it is shown that their sample paths a.s. satisfy all three pathwise…