Theory of Stochastic Processes: With Applications to Financial Mathematics and Risk Theory - Couverture rigide

Gusak, Dmytro; Kukush, Alexander; Kulik, Alexey; Mishura, Yuliya; Pilipenko, Andrey

Couverture rigide

ISBN 10 : 0387878610 ISBN 13 : 9780387878614

Editeur : Springer-Verlag New York Inc., 2009

Synopsis

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.

Détails de l'édition

• Éditeur: Springer-Verlag New York Inc.
• Date d'édition: 2009
• Langue: anglais
• ISBN 10: 0387878610
• ISBN 13: 9780387878614
• Reliure: Relié
• Nombre de pages: 388
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3,69115 Heidelberg, Germany; Heidelberg; 69115; Allemagne