Variance Reduction

Illustration weak approximation SDE

AMCS 336 Numerical Methods for Stochastic Differential Equations with connections to Machine Learning

stochastic differential equations Ito integral Monte Carlo Multilevel Monte Carlo Importance sampling Variance Reduction Kolmogorov Backward Equation Fokker-Planck equations Hamilton-Jabobi-Bellman Stochastic Optimal Control

The goal of this course is to give basic knowledge of stochastic differential equations and their numerical solution, useful for scientific and engineering modeling, guided by some problems in applications in financial mathematics, material science, geophysical flow problems, turbulent diffusion, control theory, and Monte Carlo methods.

Species count mRNA, proteins, dimers - jump processes

AMCS 308 Stochastic Numerics with Application in Simulation and Data Science

stochastic algorithms Stochastic Methods Stochastic Modeling Stochastic Optimal Control Stochastic processes Filtering theory data assimilation Monte carlo methods Variance Reduction Importance sampling

Monte Carlo methods. Simulation, estimation, data assimilation, and optimal control for time-discrete and time-continuous Markov chains