Past

We consider the problem of computing ratings using the results of games (such as chess) played between a set of n players, and show how this problem can be reduced to computing the positive eigenvectors corresponding to the dominant eigenvalues of certain n by n matrices. There is a close connection with the stationary probability distributions of certain Markov chains. In practice, if n is large, then the matrices involved will be sparse, and the power method may be used to solve the eigenvalue problems efficiently.

It is well-known that the only space-time scaling limits of Galton-Watson processes are continuous-state branching processes. Their genealogical structure is most explicitly expressed by discrete trees and R-trees, respectively. Weak limit theorems have been recently established for some of these random trees. We study here a Markovian forest growth procedure that allows to construct the genealogical forest of any continuous-state branching process with immigration as an a.s. limit of Galton-Watson forests with edge lengths. Furthermore, we are naturally led to continuous forests with edge lengths. Another strength of our method is that it yields results in the general supercritical case that was excluded in most of the previous literature.

/notices/events/abstracts/stochastic-analysis/ht05/draief.shtml

We discuss the application of gradient methods to calibrate mean reverting

stochastic volatility models. For this we use formulas based on Girsanov

transformations as well as a modification of the Bismut-Elworthy formula to

compute the derivatives of certain option prices with respect to the

parameters of the model by applying Monte Carlo methods. The article

presents an extension of the ideas to apply Malliavin calculus methods in

the computation of Greek's.

Many industrial flow problems, expecially in the minerals and process

industries, are very complex, with strong interactions between phases

and components, and with very different length and time scales. This

presentation outlines the algorithms used in the CFX-5 software, and

describes the extension of its coupled solver approach to some

multi-scale industrial problems. including Population Balance modelling

to predict size distributions of a disperse phase. These results will be

illustrated on some practical industrial problems.