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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Wahrscheinlichkeitstheorie & Statistik Continuous Parameter Markov Processes and Stochastic Differential Equations
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Continuous Parameter Markov Processes and Stochastic Differential Equations
Rabi Bhattacharya, Edward C. Waymire (Broschiert, Englisch)
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Beschreibung
This graduate text presents the elegant and profound theory of continuous parameter Markov processes and many of its applications. The authors focus on developing context and intuition before formalizing the theory of each topic, illustrated with examples. After a review of some background material, the reader is introduced to semigroup theory, including the Hille–Yosida Theorem, used to construct… continuous parameter Markov processes. Illustrated with examples, it is a cornerstone of Feller’s seminal theory of the most general one-dimensional diffusions studied in a later chapter. This is followed by two chapters with probabilistic constructions of jump Markov processes, and processes with independent increments, or Lévy processes. The greater part of the book is devoted to Itô’s fascinating theory of stochastic differential equations, and to the study of asymptotic properties of diffusions in all dimensions, such as explosion, transience, recurrence, existence of steady states, and the speed of convergence to equilibrium. A broadly applicable functional central limit theorem for ergodic Markov processes is presented with important examples. Intimate connections between diffusions and linear second order elliptic and parabolic partial differential equations are laid out in two chapters, and are used for computational purposes. Among Special Topics chapters, two study anomalous diffusions: one on skew Brownian motion, and the other on an intriguing multi-phase homogenization of solute transport in porous media. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
17.11.2024
Sprache
Englisch
EAN
9783031341533
Herausgeber
Springer International Publishing
Sonderedition
Nein
Autor
Rabi Bhattacharya, Edward C. Waymire
Seitenanzahl
506
Einbandart
Broschiert
Schlagwörter
Hille-Yoshida theorem, Lévy processes, Markov processes with jumps, Markov property, central limit theorem, infinitely divisible distributions, jump phenomena, semigroups
Thema-Inhalt
PBT - Wahrscheinlichkeitsrechnung und Statistik
PBWL - Stochastik
PBW - Angewandte Mathematik
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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