Год выпуска: 2010 Автор: Julien Guyon Издательство: LAP Lambert Academic Publishing Страниц: 172 ISBN: 9783838314464
Описание
In this book, I strove to propose a both precise and handy probabilistic modeling in some areas of finance and biology. Both fields are made of complex random systems, described by huge and noisy data, and call for expertise in probability theory and statistics. My work is a contribution to modeling interactions in such systems, numerical analysis of the models, and statistical analysis of experimental data. In finance, I first focus on analysis of weak error of the density of the Euler scheme for stochastic differential equations, deriving new expansions in Gaussian-like functional spaces. Then I study ergodic properties of stochastic volatility models, with extended numerical experiments. In biology, I work on cellular aging, suggesting a bifurcating autoregressive model to describe growth rates of cells and building statistical procedures to estimate parameters and test biological hypothesis. To this end, I introduce the concept of bifurcating Markov chains and prove that such...
