Functional Analysis for Probability and Stochastic Processes ICM edition: An Introduction

Science & Math

Bobrowski, Adam

Mathematics

Cambridge University Press

Functional Analysis for Probability and Stochastic Processes: An Introduction

Designed for students of probability and stochastic processes, as well as for students of functional analysis, specifically, this volume presents some chosen parts of functional analysis that can help clarify probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook or for self-study.

Earth Sciences

Functional Analysis Revisited: An Essay on Completeness

Functional Analysis Revisited

'Functional Analysis Revisited' is not a first course in functional analysis - although it covers the basic notions of functional analysis, it assumes the reader is somewhat acquainted with them. It is by no means a second course either: there are too many deep subjects that are not within scope here. Instead, having the basics under his belt, the author takes the time to carefully think through their fundamental consequences. In particular, the focus is on the notion of completeness and its implications, yet without venturing too far from areas where the description 'elementary' is still valid. The author also looks at some applications, perhaps just outside the core of functional analysis, that are not completely trivial. The aim is to show how functional analysis influences and is influenced by other branches of contemporary mathematics. This is what we mean by 'Functional Analysis Revisited.'

This book presents a detailed and contemporary account of the classical theory of convergence of semigroups and its more recent development treating the case where the limit semigroup, in contrast to the approximating semigroups, acts merely on a subspace of the original Banach space (this is the case, for example, with singular perturbations). The author demonstrates the far-reaching applications of this theory using real examples from various branches of pure and applied mathematics, with a particular emphasis on mathematical biology. The book may serve as a useful reference, containing a significant number of new results ranging from the analysis of fish populations to signaling pathways in living cells. It comprises many short chapters, which allows readers to pick and choose those topics most relevant to them, and it contains 160 end-of-chapter exercises so that readers can test their understanding of the material as they go along.

Convergence of One-Parameter Operator Semigroups: In Models of Mathematical Biology and Elsewhere (New Mathematical Monographs, Series Number 30)

Elementary treatments of Markov chains, especially those devoted to discrete-time and finite state-space theory, leave the impression that everything is smooth and easy to understand. This exposition of the works of Kolmogorov, Feller, Chung, Kato, and other mathematical luminaries, which focuses on time-continuous chains but is not so far from being elementary itself, reminds us again that the impression is false: an infinite, but denumerable, state-space is where the fun begins. If you have not heard of Blackwell's example (in which all states are instantaneous), do not understand what the minimal process is, or do not know what happens after explosion, dive right in. But beware lest you are enchanted: 'There are more spells than your commonplace magicians ever dreamed of.'

Generators of Markov Chains: From a Walk in the Interior to a Dance on the Boundary (Cambridge Studies in Advanced Mathematics, Series Number 190)

This authored monograph presents a mathematical description of the time evolution of neutral genomic regions in terms of the differential Lyapunov equation. The qualitative behavior of its solutions, with respect to different mutation models and demographic patterns, can be characterized using operator semi group theory.
Mutation and drift are two of the main genetic forces, which act on genes of individuals in populations. Their effects are influenced by population dynamics. This book covers the application to two mutation models: single step mutation for microsatellite loci and single-base substitutions. The effects of demographic change to the asymptotic of the distribution are also covered. The target audience primarily covers researchers and experts in the field but the book may also be beneficial for graduate students.

An Operator Semigroup in Mathematical Genetics (SpringerBriefs in Applied Sciences and Technology)

Kimmel, Marek

Biological Sciences

Springer

See the best price to sell, buy, or rent books by Bobrowski, Adam. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Bobrowski, Adam

See the best price to sell, buy, or rent books by Bobrowski, Adam. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Functional Analysis for Probability and Stochastic Processes ICM edition: An Introduction

Functional Analysis for Probability and Stochastic Processes: An Introduction

Functional Analysis for Probability and Stochastic Processes: An Introduction

Functional Analysis Revisited

Functional Analysis Revisited: An Essay on Completeness

Convergence of One-Parameter Operator Semigroups: In Models of Mathematical Biology and Elsewhere (New Mathematical Monographs, Series Number 30)

Generators of Markov Chains: From a Walk in the Interior to a Dance on the Boundary (Cambridge Studies in Advanced Mathematics, Series Number 190)

An Operator Semigroup in Mathematical Genetics (SpringerBriefs in Applied Sciences and Technology)