Dmytro Gusak

(Author)

Theory of Stochastic Processes: With Applications to Financial Mathematics and Risk Theory (2010)Paperback - 2010, 3 May 2012

Theory of Stochastic Processes: With Applications to Financial Mathematics and Risk Theory (2010)
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Part of Series
Problem Books in Mathematics
Print Length
376 pages
Language
English
Publisher
Springer
Date Published
3 May 2012
ISBN-10
1461425069
ISBN-13
9781461425069

Description

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.

Product Details

Authors:
Dmytro GusakAlexander KukushAlexey KulikYuliya MishuraAndrey Pilipenko
Book Edition:
2010
Book Format:
Paperback
Country of Origin:
NL
Date Published:
3 May 2012
Dimensions:
23.39 x 15.6 x 2.03 cm
ISBN-10:
1461425069
ISBN-13:
9781461425069
Language:
English
Location:
New York, NY
Pages:
376
Publisher:
Weight:
539.77 gm

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