Introduction to Monte-Carlo Methods for Transport and Diffusion Equations

Monte-Carlo methods is the generic term given to numerical methods that use sampling of random numbers. This text is aimed at graduate students in mathematics, physics, engineering, economics, finance and the biosciences that are interested in using Monte-Carlo methods for the resolution of partial differential equations, transport equations, the Boltzmann equation and the parabolic equations of diffusion. It includes applied examples, particularly in mathematical finance, along with discussion of the limits of the methods and description of specific techniques used in practice for each example.