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Measure Theory, Probability, and Stochastic Processes
Af: Jean-Francois Le Gall Engelsk Hardback
SPAR
kr 150
Measure Theory, Probability, and Stochastic Processes
Af: Jean-Francois Le Gall Engelsk Hardback

This textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian motion and harmonic functions on the other, this book provides an introduction to the rich interplay between probability and other areas of analysis.

Arranged into three parts, the book begins with a rigorous treatment of measure theory, with applications to probability in mind. The second part of the book focuses on the basic concepts of probability theory such as random variables, independence, conditional expectation, and the different types of convergence of random variables. In the third part, in which all chapters can be read independently, the reader will encounter three important classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter ends with a selection of illuminating exercises of varying difficulty. Some basic facts from functional analysis, in particular on Hilbert and Banach spaces, are included in the appendix.

Measure Theory, Probability, and Stochastic Processes is an ideal text for readers seeking a thorough understanding of basic probability theory. Students interested in learning more about Brownian motion, and other continuous-time stochastic processes, may continue reading the author’s more advanced textbook in the same series (GTM 274).


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This textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian motion and harmonic functions on the other, this book provides an introduction to the rich interplay between probability and other areas of analysis.

Arranged into three parts, the book begins with a rigorous treatment of measure theory, with applications to probability in mind. The second part of the book focuses on the basic concepts of probability theory such as random variables, independence, conditional expectation, and the different types of convergence of random variables. In the third part, in which all chapters can be read independently, the reader will encounter three important classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter ends with a selection of illuminating exercises of varying difficulty. Some basic facts from functional analysis, in particular on Hilbert and Banach spaces, are included in the appendix.

Measure Theory, Probability, and Stochastic Processes is an ideal text for readers seeking a thorough understanding of basic probability theory. Students interested in learning more about Brownian motion, and other continuous-time stochastic processes, may continue reading the author’s more advanced textbook in the same series (GTM 274).


Produktdetaljer
Sprog: Engelsk
Sider: 406
ISBN-13: 9783031142048
Indbinding: Hardback
Udgave:
ISBN-10: 3031142047
Udg. Dato: 30 okt 2022
Længde: 27mm
Bredde: 160mm
Højde: 242mm
Oplagsdato: 30 okt 2022
Forfatter(e): Jean-Francois Le Gall
Forfatter(e) Jean-Francois Le Gall


Kategori Integralregning og integralligninger


Sprog Engelsk


Indbinding Hardback


Sider 406


Udgave


Længde 27mm


Bredde 160mm


Højde 242mm


Udg. Dato 30 okt 2022


Oplagsdato 30 okt 2022

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