Related papers: Solving Stochastic Differential Equations with Jum…

The possibility of different interpretations of the stochastic term (or calculi) in the overdamped Langevin equation for the motion of a particle in an inhomogeneous medium is often referred to as the "Ito--Stratonovich dilemma," although…

This paper seeks an efficient algorithm for stochastic precoding to maximize the long-term average weighted sum rates throughout a multiple-input multiple-output (MIMO) network. Unlike many existing works that assume a particular…

As a simplified model for subsurface flows elliptic equations may be utilized. Insufficient measurements or uncertainty in those are commonly modeled by a random coefficient, which then accounts for the uncertain permeability of a given…

A Monte-Carlo approach to solving a stochastic jump transition model for active-region energy (Wheatland and Glukhov, Astrophys. J. 494, 1998; Wheatland, Astrophys. J. 679, 2008) is described. The new method numerically solves the…

We investigate the behaviour of stochastic differential equations, especially Burgers' eq., by means of Monte-Carlo-techniques.

Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…

We present an adaptive multilevel Monte Carlo algorithm for solving the stochastic drift-diffusion-Poisson system with non-zero recombination rate. The a-posteriori error is estimated to enable goal-oriented adaptive mesh refinement for the…

We consider a couple of integrodifferential PDEs arising from a stochastic Markovian control problem subjected to initial-terminal conditions. These equations correspond to the MFG system for a controlled jump-diffusion process. We prove…

This article presents a simple but effective and efficient approach to improve the accuracy and stability of Least-Squares Monte Carlo. The key idea is to construct the ansatz of conditional expected continuation payoff using the…

We propose in this work a Monte Carlo method for three dimensional scalar radiative transfer equations with non-integrable, space-dependent scattering kernels. Such kernels typically account for long-range statistical features, and arise…

We consider the first-crossing-time problem through a constant boundary for a Wiener process perturbed by random jumps driven by a counting process. On the base of a sample-path analysis of the jump-diffusion process we obtain explicit…

With the goal to provide absolute lower bounds for the best possible running times that can be achieved by $(1+\lambda)$-type search heuristics on common benchmark problems, we recently suggested a dynamic programming approach that computes…

We derive some rather general, but complicated, formulae to compute the survival function and the first passage time distribution of the $n^\text{th}$ coordinate of a many-body stochastic process in the presence of a killing barrier. First…

We address the problem of minimizing the expected first-passage time of a Brownian motion with Poissonian resetting, with respect to the resetting rate $r.$ We consider both the one-boundary and the two-boundary cases.We investigate the…

To achieve efficient and accurate long-time integration, we propose a fast, accurate, and stable high-order numerical method for solving fractional-in-space reaction-diffusion equations. The proposed method is explicit in nature and…

In the field of nuclear reactor physics, transient phenomena are usually studied using deterministic or hybrids methods. These methods require many approximations, such as: geometry, time and energy discretizations, material homogenization…

This work focuses on stability analysis of numerical solutions to jump diffusions and jump diffusions with Markovian switching. Due to the use of Poisson processes, using asymptotic expansions as in the usual approach of treating diffusion…

How long does it take a random walker to reach a given target point? This quantity, known as a first passage time (FPT), has led to a growing number of theoretical investigations over the last decade1. The importance of FPTs originates from…

We present a numerical procedure of solving the subdiffusion equation with Caputo fractional time derivative. On the basis of few examples we show that the subdiffusion is a 'long time memory' process and the short memory principle should…

We consider a Markovian jumping process with two absorbing barriers, for which the waiting-time distribution involves a position-dependent coefficient. We solve the Fokker-Planck equation with boundary conditions and calculate the mean…