Stochastic Representation and Monte Carlo Simulation for Multiterm Time-Fractional Diffusion Equation

Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation.

We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Lévy alpha -stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter Mittag-Leffler...

Stochastic Simulation,monte Carlo Methods and Applications1

Stochastic Simulation and Monte Carlo Methods

In these lecture notes we will work through three different computational problems from different application areas. We will simulate the irregular motion of a particle in an environment of smaller solvent molecules, we will study a biochemical control network and we will compute a numerical approximation to a high dimensional integral. Even though these three problems are different, and the wa...

Fractional Langevin Monte Carlo: Exploring Levy Driven Stochastic Differential Equations for Markov Chain Monte Carlo

Along with the recent advances in scalable Markov Chain Monte Carlo methods, sampling techniques that are based on Langevin diffusions have started receiving increasing attention. These so called Langevin Monte Carlo (LMC) methods are based on diffusions driven by a Brownian motion, which gives rise to Gaussian proposal distributions in the resulting algorithms. Even though these approaches hav...

Stochastic Programming by Monte Carlo Simulation Methods

We consider in this paper stochastic programming problems which can be formulated as an optimization problem of an expected value function subject to deterministic constraints. We discuss a Monte Carlo simulation approach based on sample average approximations to a numerical solution of such problems. In particular, we give a survey of a statistical inference of the sample average estimators of...