相关论文: Time discretization and Markovian iteration for co…

We present a new efficient computational approach for time-dependent first-order Hamilton-Jacobi-Bellman PDEs. Since our method is based on a time-implicit Eulerian discretization, the numerical scheme is unconditionally stable, but…

The first order by time partial differential equations are used as models in applications such as fluid flow, heat transfer, solid deformation, electromagnetic waves, and others. In this paper we propose the new numerical method to solve a…

We give local and global existence and uniqueness results for systems of coupled FBSDEs in the multidimensional setting and with generators allowed to grow arbitrarily fast in the control variable. Our results are based on Malliavin…

In this paper, we propose a deep learning based numerical scheme for strongly coupled FBSDEs, stemming from stochastic control. It is a modification of the deep BSDE method in which the initial value to the backward equation is not a free…

We introduce a predictor-corrector discretisation scheme for the numerical integration of a class of stochastic differential equations and prove that it converges with weak order 1.0. The key feature of the new scheme is that it builds up…

A novel efficient and high accuracy numerical method for the time-fractional differential equations (TFDEs) is proposed in this work. We show the equivalence between TFDEs and the integer-order extended parametric differential equations…

Bayesian analysis methods often use some form of iterative simulation such as Monte Carlo computation. Models that involve discrete variables can sometime pose a challenge, either because the methods used do not support such variables (e.g.…

Convergence analysis of Markov chain Monte Carlo methods in high-dimensional statistical applications is increasingly recognized. In this paper, we develop general mixing time bounds for Metropolis-Hastings algorithms on discrete spaces by…

We present a new approach to parallelization of the first-order backward difference discretization (BDF1) of the time derivative in partial differential equations, such as the nonlinear heat and viscous Burgers equations. The time…

This paper introduces a sparse matrix discrete interpolation method to effectively compute matrix approximations in the reduced order modeling framework. The sparse algorithm developed herein relies on the discrete empirical interpolation…

A framework for exponential time discretization of the multilayer rotating shallow water equations is developed in combination with a mimetic discretization in space. The method is based on a combination of existing exponential time…

We study the weak approximation of the second-order backward SDEs (2BSDEs), when the continuous driving martingales are approximated by discrete time martingales. We establish a convergence result for a class of 2BSDEs, using both…

High order methods have shown great potential to overcome performance issues of simulations of partial differential equations (PDEs) on modern hardware, still many users stick to low-order, matrix-based simulations, in particular in porous…

In this work, we study dynamic programming (DP) algorithms for partially observable Markov decision processes with jointly continuous and discrete state-spaces. We consider a class of stochastic systems which have coupled discrete and…

The paper proposes an algorithm for a discretization (sampled-time implementation) of a homogeneous control preserving the finite-time and nearly fixed-time stability property of the original (sampling-free) system. The sampling period is…

We study the discrete-time approximation for solutions of quadratic forward back- ward stochastic differential equations (FBSDEs) driven by a Brownian motion and a jump process which could be dependent. Assuming that the generator has a…

Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those…

Filtering---estimating the state of a partially observable Markov process from a sequence of observations---is one of the most widely studied problems in control theory, AI, and computational statistics. Exact computation of the posterior…

The discrete class algorithm presented in this paper is an efficient simulation tool for stochastic processes governed by a reasonably small set of transition rates. The algorithm is presented, its performance compared to prevailing methods…

A majorized accelerated block coordinate descent (mABCD) method in Hilbert space is analyzed to solve a sparse PDE-constrained optimization problem via its dual. The finite element approximation method is investigated. The attractive…