Год выпуска: 2010 Автор: Huizhong Wu and John A. D. Appleby Издательство: LAP Lambert Academic Publishing Страниц: 200 ISBN: 9783838360447
Описание
This work deals with the asymptotic behaviour of highly nonlinear stochastic differential equations, as well as linear and nonlinear functional differential equations. Both ordinary functional and neutral equations are analysed. In the first chapter, a class of nonlinear SDEs (mainly scaler equations) which satisfy the Law of the Iterated Logarithm is studied, and the results applied to a financial market model. The second chapter deals with a more general class of finite-dimensional nonlinear SDEs and SFDEs, employing comparison and time change methods, as well as martingale inequalities, to determine the almost sure rate of growth of the running maximum of functionals of the solution. The third chapter examines the exact almost sure rate of growth of the large deviations for affine SFDEs, and for equations with additive noise which are subject to relatively weak nonlinearities at infinity. The fourth chapter extends conventional conditons for existence and uniqueness of...
