An introduction to probabilistic methods with applications

An Introduction to Probabilistic Methods with Applications

This special volume of the ESAIM Journal, Mathematical Modelling and Numerical Analysis, contains a collection of articles on probabilistic interpretations of some classes of nonlinear integrodifferential equations. The selected contributions deal with a wide range of topics in applied probability theory and stochastic analysis, with applications in a variety of scientific disciplines, includin...

Particle methods: An introduction with applications

Interacting particle methods are increasingly used to sample from complex high-dimensional distributions. They have found a wide range of applications in applied probability, Bayesian statistics and information engineering. Understanding rigorously these new Monte Carlo simulation tools leads to fascinating mathematics related to Feynman-Kac path integral theory and their interacting particle i...

An Introduction to Particle Methods with Financial Applications

The aim of this article is to give a general introduction to the theory of interacting particle methods, and an overview of its applications to computational finance. We survey the main techniques and results on interacting particle systems and explain how they can be applied to the numerical solution of a variety of financial applications such as pricing complex path dependent European options...

An Introduction to Probabilistic Automata

This paper provides an elementary introduction to the probabilistic automaton (PA) model, which has been developed by Segala. We describe how distributed systems with discrete probabilities can be modeled and analyzed by means of PAs. We explain how the basic concepts for the analysis of nonprobabilistic automata can be extended to probabilistic systems. In particular, we treat the parallel com...

An Introduction to Sociolinguistics