Convolution-like Structures, Differential Operators and Diffusion Processes

This book explores the construction of convolution-like operators on probability measures, highlighting the connections between harmonic analysis,probability theory,and differential equations. It is valuable for graduate students and researchers in these fields.

Format: Paperback / softback
Length: 262 pages
Publication date: 28 July 2022
Publisher: Springer International Publishing AG

This comprehensive text delves into the latest advancements in the field of generalized harmonic analysis, exploring its profound connections with convolutions, differential operators, and diffusion processes. It is widely recognized that these interconnected concepts hold immense significance, with the ordinary convolution commuting with the Laplacian and the law of Brownian motion exhibiting a convolution semigroup property with respect to the ordinary convolution. Motivated by the desire to extend this valuable connection and its practical applications in probability theory, the book specifically focuses on the central question of constructing convolution-like operators on the space of probability measures on a metric space, with the aim of preserving the law of the diffusion process under such operators. Through a detailed analysis, the text highlights the intricate interplay between the construction of convolution-like structures and diverse disciplines such as stochastic processes, ordinary and partial differential equations, spectral theory, special functions, and integral transforms. This book is an invaluable resource for advanced graduate students and researchers seeking to delve into the intricate intersections between harmonic analysis, probability theory, and differential equations. Its comprehensive coverage and insightful insights make it a must-read for anyone interested in advancing their understanding of these complex mathematical topics.

Weight: 427g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031052958
Edition number: 1st ed. 2022