Dmytro Gusak: Theory of Stochastic Processes

Cover: 9781461425069 | Theory of Stochastic Processes | Dmytro Gusak (u. a.) | Taschenbuch

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Beschreibung

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.

Zusammenfassung

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: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2012
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Problem Books in Mathematics
Inhalt:	xii 376 S. 8 s/w Illustr. 376 p. 8 illus.
ISBN-13:	9781461425069
ISBN-10:	1461425069
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Gusak, Dmytro Kukush, Alexander Kulik, Alexey Mishura, Yuliya Pilipenko, Andrey
Hersteller:	Humana Springer Springer US, New York, N.Y. Problem Books in Mathematics
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 21 mm
Von/Mit:	Dmytro Gusak (u. a.)
Erscheinungsdatum:	03.05.2012
Gewicht:	0,587 kg