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Theory of Stochastic Processes, 2010 With Applications to Financial Mathematics and Risk Theory Problem Books in Mathematics Series

Langue : Anglais

Auteurs :

Couverture de l’ouvrage Theory of Stochastic Processes

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 necessary for deeper understanding of the main topics in the theory of stochastic processes and its related fields.

The book is divided into chapters according to the various topics. Each chapter contains problems, hints, solutions, as well as a self-contained theoretical part which gives all the necessary material for solving the problems. References to the literature are also given.

The exercises have various levels of complexity and vary from simple ones, useful for students studying basic notions and technique, to very advanced ones that reveal some important theoretical facts and constructions.

This book is one of the largest collections of problems in the theory of stochastic processes and its applications. The problems in this book can be useful for undergraduate and graduate students, as well as for specialists in the theory of stochastic processes.

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.

Contains over 1000 high quality exercises on stochastic processes

Presents a modern approach to topics such as sample paths and optimal stopping

Ideal for professors who need exercises for exams, and graduate students wishing to learn about stochastic processes

Includes supplementary material: sn.pub/extras

Date de parution :

Ouvrage de 376 p.

15.5x23.5 cm

Sous réserve de disponibilité chez l'éditeur.

Prix indicatif 52,74 €

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Date de parution :

Ouvrage de 376 p.

15.5x23.5 cm

Disponible chez l'éditeur (délai d'approvisionnement : 15 jours).

Prix indicatif 52,74 €

Ajouter au panier