Related papers: Direct Numerical Solutions to Stochastic Different…

This paper is concerned with stochastic incompressible Navier-Stokes equations with multiplicative noise in two dimensions with respect to periodic boundary conditions. Based on the Helmholtz decomposition of the multiplicative noise,…

In this paper it is shown how to solve numerically eigenvalue problems associated to second order linear ordinary differential equations, containing also terms which depend on the variable. A didactic presentation of the Numerov Method is…

This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…

For stochastic evolution equations with fractional derivatives, classical solutions exist when the order of the time derivative of the unknown function is not too small compared to the order of the time derivative of the noise; otherwise,…

In this article we present a way of treating stochastic partial differential equations with multiplicative noise by rewriting them as stochastically perturbed evolutionary equations in the sense of \cite{picardbook}, where a general…

In this paper a drift-randomized Milstein method is introduced for the numerical solution of non-autonomous stochastic differential equations with non-differentiable drift coefficient functions. Compared to standard Milstein-type methods we…

This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the…

Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…

A new method is described for constructing a generalized solution for stochastic differential equations. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and provides a unified framework for the study of…

A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the…

In this paper we show the existence and uniqueness of a solution for a stochastic differential equation driven by an additive noise which is the sum of two fractional Brownian motions with different Hurst parameters. The proofs are based on…

This thesis presents new mathematical algorithms for the numerical solution of a mathematical problem class called \emph{dynamic optimization problems}. These are mathematical optimization problems, i.e., problems in which numbers are…

We propose an approximation of nonlinear renewal equations by means of ordinary differential equations. We consider the integrated state, which is absolutely continuous and satisfies a delay differential equation. By applying the…

We are concerned with the numerical resolution of backward stochastic differential equations. We propose a new numerical scheme based on iterative regressions on function bases, which coefficients are evaluated using Monte Carlo…

We study stochastic optimization from a joint continuous-discrete point of view. Starting from a second-order stochastic differential equation interpreted as a noisy accelerated gradient flow, we discretize the dynamics by a fully implicit…

We consider a higher-order Milstein scheme for stochastic partial differential equations with trace class noise which fulfill a certain commutativity condition. A novel technique to generally improve the order of convergence of Taylor…

In the pathwise stochastic calculus framework, the paper deals with the general study of equations driven by an additive Gaussian noise, with a drift function having an infinite limit at point zero. An ergodic theorem and the convergence of…

The present era of quantum processors with hundreds to thousands of noisy qubits has sparked interest in understanding the computational power of these devices and how to leverage it to solve practically relevant problems. For applications…

In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian Stochastic Schr\"odinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are…

This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schr\"odinger equation inspired by stochastic mechanics and generative diffusion models. Unlike existing approaches, which exhibit…