Theory of stochastic processes : with applications to financial mathematics and risk theory
This book is a collection of exercises covering all the main topics in the modern theory of stochastic processes and its applications, including finance, actuarial mathematics, queuing theory, and risk theory. The aim of this book is to provide the reader with the theoretical and practical material...
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Édition: | 1. |
| Collection: | Problem Books in Mathematics
|
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Theory of stochastic processes, with applications to financial mathematics and risk theory, Dmytro Gusak, Alexander Kukush, Alexey Kulik, ... [et al.], 2010, New York, Springer, 1 vol. (XII-375 p.), Problem books in mathematics, 978-0-387-87861-4 • Theory of Stochastic Processes, Texte imprimé, 9781461425069 • Theory of Stochastic Processes, Texte imprimé, 9780387879376 • Theory of Stochastic Processes, Texte imprimé, 9781071605165 |
Table des matières:
- Definition of stochastic process. Cylinder #x03C3;-algebra, finite-dimensional distributions, the Kolmogorov theorem Characteristics of a stochastic process. Mean and covariance functions. Characteristic functions Trajectories. Modifications. Filtrations Continuity. Differentiability. Integrability Stochastic processes with independent increments. Wiener and Poisson processes. Poisson point measures Gaussian processes Martingales and related processes in discrete and continuous time. Stopping times Stationary discrete- and continuous-time processes. Stochastic integral over measure with orthogonal values Prediction and interpolation Markov chains: Discrete and continuous time Renewal theory. Queueing theory Markov and diffusion processes It#x00F4; stochastic integral. It#x00F4; formula. Tanaka formula Stochastic differential equations Optimal stopping of random sequences and processes Measures in a functional spaces. Weak convergence, probability metrics. Functional limit theorems Statistics of stochastic processes Stochastic processes in financial mathematics (discrete time) Stochastic processes in financial mathematics (continuous time) Basic functionals of the risk theory