Using Stochastic Approaches for Teaching Mass Transfer Unit Operations: The Monte Carlo Method

Dynamical Monte Carlo method for stochastic epidemic models

In this work we introduce a new approach to Dynamical Monte Carlo methods to simulate markovian processes. We apply this approach to formulate and study an epidemic generalized SIRS model. The results are in excellent agreement with the fourth order Runge-Kutta method in a region of deterministic solution. Introducing local stochastic interactions, the Runge-Kutta method is no longer applicable...

Stabilized multilevel Monte Carlo method for stiff stochastic differential equations

A multilevel Monte Carlo (MLMC) method for mean square stable stochastic differential equations with multiple scales is proposed. For such problems, that we call stiff, the performance of MLMC methods based on classical explicit methods deteriorates because of the time step restriction to resolve the fastest scales that prevents to exploit all the levels of the MLMC approach. We show that by sw...

Fast Monte Carlo Algorithms for Tensor Operations

We consider scalable randomized algorithms for many common tensor operations, including tensor multiplication, low-rank decomposition and nuclear norm minimization. Such operations arise in a number of modern day applications of tensors in machine learning and signal processing. Specifically, we introduce polynomial time algorithms that employ a small number of lateral and/or horizontal slices ...

Nonlinear Stochastic Optimization by the Monte-Carlo Method

Methods for solving stochastic optimization problems by Monte-Carlo simulation are considered. The stoping and accuracy of the solutions is treated in a statistical manner, testing the hypothesis of optimality according to statistical criteria. A rule for adjusting the Monte-Carlo sample size is introduced to ensure the convergence and to find the solution of the stochastic optimization problem...

The Monte-Carlo Method