Related papers: A symmetry-adapted numerical scheme for SDEs

In this paper, we further consider the symmetry-based method for seeking nonlocally related systems for partial differential equations. In particular, we show that the symmetry-based method for partial differential equations is the natural…

The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators suggests that formal uncertainty quantification can also be performed in this context. Competing statistical…

We define some approximation schemes for different kinds of generalized backward stochastic differential systems, considered in the Markovian framework. We propose a mixed approximation scheme for a decoupled system of forward reflected SDE…

This paper introduces a new approximation scheme for solving high-dimensional semilinear partial differential equations (PDEs) and backward stochastic differential equations (BSDEs). First, we decompose a target semilinear PDE (BSDE) into…

We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…

Nonlinear ODEs invariant under the group SL(2,R) are solved numerically. We show that solution methods incorporating the Lie point symmetries provide better results than standard methods.

In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are…

In this paper, we present new results on the Riemannian geometry of symmetric positive semi-definite (SPSD) matrices. First, based on an existing approximation of the geodesic path, we introduce approximations of the logarithmic and…

In this paper, we propose a method, that is based on equivariant moving frames, for development of high order accurate invariant compact finite difference schemes that preserve Lie symmetries of underlying partial differential equations. In…

Popular deterministic approximations of posterior distributions from, e.g. the Laplace method, variational Bayes and expectation-propagation, generally rely on symmetric approximating families, often taken to be Gaussian. This choice…

This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…

We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…

Symmetry is a powerful tool for finding analytical solutions to differential equations, both partial and ordinary, via the similarity variables or via the invariance of the equation under group transformations. It is the largest group of…

This paper presents a simple numerical scheme for the two dimensional Shallow-Water Equations (SWEs). Inspired by the study of numerical approximation of the one dimensional SWEs Audusse et al. (2015), this paper extends the problem from 1D…

We present a method for approximating solutions of Stochastic Differential Equations (SDEs) with arbitrary rates. This approximation is derived for bounded and measurable test functions. Specifically, we demonstrate that, leveraging the…

Stochastic Gradient Descent (SGD) is one of the most popular algorithms in statistical and machine learning due to its computational and memory efficiency. Various averaging schemes have been proposed to accelerate the convergence of SGD in…

The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward…

We describe an Euler scheme to approximate solutions of L\'evy driven Stochastic Differential Equations (SDE) where the grid points are random and given by the arrival times of a Poisson process. This result extends a previous work of the…

The widely used Heun algorithm for the numerical integration of stochastic differential equations (SDEs) is critically re-examined. We discuss and evaluate several alternative implementations, motivated by the fact that the standard Heun…

Although the governing equations of many systems, when derived from first principles, may be viewed as known, it is often too expensive to numerically simulate all the interactions they describe. Therefore researchers often seek simpler…