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Continuous Parameter Markov Processes and Stochastic Differential Equations (Graduate Texts in Mathematics, 299) free ebook download

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Author(s):	Rabi Bhattacharya

Date:	2024	Format:	pdf	Language:	English	ISBN/ASIN:	3031332946
Pages:	521	OCR:		Quality:		ISBN13:
Uploader:	gestalt	Upload Date:	11/28/2023 5:43:41 PM

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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 HilleYosida Theorem, used to construct continuous parameter Markov processes. Illustrated with examples, it is a cornerstone of Fellers 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 Lvy processes. The greater part of the book is devoted to Its 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.
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Tags: Continuous Differential Equations Graduate Markov Mathematics Parameter Processes Stochastic Texts

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Continuous Parameter Markov Processes and Stochastic Differential Equations (Graduate Texts in Mathematics, 299) free ebook download

Category: Mathematics

Description: Click to see full description

Category:
Mathematics