Related papers: Discrete Feynman-Kac approximation for parabolic A…
The Feynman-Kac equations are a type of partial differential equations describing the distribution of functionals of diffusive motion. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, being a…
We consider the thermally activated escape of an overdamped Brownian particle over a potential barrier in the presence of periodic driving. A time-dependent path-integral formalism is developed which allows us to derive asymptotically exact…
In this paper, we propose a novel data-driven framework for discovering probabilistic laws underlying the Feynman-Kac formula. Specifically, we introduce the first stochastic SINDy method formulated under the risk-neutral probability…
We study a class of fully-discrete schemes for the numerical approximation of solutions of stochastic Cahn--Hilliard equations with cubic nonlinearity and driven by additive noise. The spatial (resp. temporal) discretization is performed…
We formulate an initial- and Dirichlet boundary- value problem for a linear stochastic heat equation, in one space dimension, forced by an additive space-time white noise. First, we approximate the mild solution to the problem by the…
The aim of this work is to provide the strong convergence results of numerical approximations of a general second order non-autonomous semilinear stochastic partial differential equation (SPDE) driven simultaneously by an additive…
We present a Feynman-Kac formula for the $1$-dimensional stochastic heat equation (SHE) driven by a time-homogeneous Gaussian white noise potential, where the noise is interpreted in the Wick-It\^o-Skorokhod sense. Our approach consists in…
The aim of this paper is to establish the almost sure asymptotic behavior as the space variable becomes large, for the solution to the one spatial dimensional stochastic heat equation driven by a Gaussian noise which is white in time and…
In this paper we consider Galerkin-finite element methods that approximate the solutions of initial-boundary-value problems in one space dimension for parabolic and Schr\"odinger evolution equations with dynamical boundary conditions. Error…
In this article, we consider the stochastic wave equation on the real line driven by a linear multiplicative Gaussian noise, which is white in time and whose spatial correlation corresponds to that of a fractional Brownian motion with Hurst…
In this paper, we present a novel Feynman-Kac formula and investigate learning-based methods for approximating general nonlinear time-dependent Schr\"odinger equations which may be high-dimensional. Our formulation integrates both the…
In this work we study the numerical approximation of a class of ergodic Backward Stochastic Differential Equations. These equations are formulated in an infinite horizon framework and provide a probabilistic representation for elliptic…
One of the outstanding problems in the numerical discretization of the Feynman-Kac formula calls for the design of arbitrary-order short-time approximations that are constructed in a stable way, yet only require knowledge of the potential…
In this article, we present the mathematical analysis of the convergence of the linearized Crank-Nicolson Galerkin method for a nonlinear Schrodinger problem related to a domain with a moving boundary. The convergence analysis of the…
We analyze the effect of additive fractional noise with Hurst parameter $H > \frac{1}{2}$ on fast-slow systems. Our strategy is based on sample paths estimates, similar to the approach by Berglund and Gentz in the Brownian motion case. Yet,…
In this work, we propose a method for solving Kolmogorov hypoelliptic equations based on Fourier transform and Feynman-Kac formula. We first explain how the Feynman-Kac formula can be used to compute the fundamental solution to parabolic…
We implement a Laplace method for the renormalised solution to the generalised 2D Parabolic Anderson Model (gPAM) driven by a small spatial white noise. Our work rests upon Hairer's theory of regularity structures which allows to generalise…
We provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the…
This short note is devoted to establishing the almost sure central limit theorem for the parabolic/hyperbolic Anderson models driven by colored-in-time Gaussian noises, completing recent results on quantitative central limit theorems for…
In this paper we establish a best approximation property of fully discrete Galerkin finite element solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty$ norm. The discretization method…