相关论文: A regression-based Monte Carlo method to solve bac…

A numerical approach for the approximation of inertial manifolds of stochastic evolutionary equations with multiplicative noise is presented and illustrated. After splitting the stochastic evolutionary equations into a backward and a…

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively.…

We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of…

This paper presents a new method for the solution of multiscale stochastic differential equations at the diffusive time scale. In contrast to averaging-based methods, e.g., the heterogeneous multiscale method (HMM) or the equation-free…

In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that…

The use of sequential Monte Carlo within simulation for path-dependent option pricing is proposed and evaluated. Recently, it was shown that explicit solutions and importance sampling are valuable for efficient simulation of spot price and…

Modeling physical phenomena like heat transport and diffusion is crucially dependent on the numerical solution of partial differential equations (PDEs). A PDE solver finds the solution given coefficients and a boundary condition, whereas an…

The application of the approximation-operational approach to solving linear differential equations of fractional order with variable coefficients is considered. It is shown that the method can also be applied to solving differential…

The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…

We present new stochastic differential equations, that are more general and simpler than the existing Ito-based stochastic differential equations. As an example, we apply our approach to the investment (portfolio) model.

Modern macroeconometrics often relies on time series models for which it is time-consuming to evaluate the likelihood function. We demonstrate how Bayesian computations for such models can be drastically accelerated by reweighting and…

In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…

A method is presented to tackle the sign problem in the simulations of systems having indefinite or complex-valued measures. In general, this new approach is shown to yield statistical errors smaller than the crude Monte Carlo using…

In the present work, firstly, we use a minimax equality to prove the existence of a solution of certain system of varitional equations and we provide a numerical approximation of such a solution. Then, we propose a numerical method to solve…

Stochastic partial differential equations (SPDEs) are often difficult to solve numerically due to their low regularity and high dimensionality. These challenges limit the practical use of computer-aided studies and pose significant barriers…

Diagrammatic Monte Carlo approach is applied to a problem of a single spin-down fermion resonantly interacting with the sea of ideal spin-up fermions. On one hand, we develop a generic, sign-problem tolerant, method of exact numerical…

We apply multilevel Monte Carlo for option pricing problems using exponential L\'{e}vy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate…

Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…

We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where…

In this paper we consider the numerical solution of Fractional Differential Equations by means of $m$-step recursions. The construction of such formulas can be obtained in many ways. Here we study a technique based on the rational…