Convolution-like Structures, Differential Operators and Diffusion Processes

Released on by Rúben Sousa
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  • Convolution-like Structures, Differential Operators and Diffusion Processes Book Detail

  • Author : Rúben Sousa
  • Release Date : 2022-07-27
  • Publisher : Springer Nature
  • Genre : Mathematics
  • Pages : 269
  • ISBN 13 : 303105296X
  • File Size : 64,64 MB
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Convolution-like Structures, Differential Operators and Diffusion Processes by Rúben Sousa PDF Summary

Book Description: T​his book provides an introduction to recent developments in the theory of generalized harmonic analysis and its applications. It is well known that convolutions, differential operators and diffusion processes are interconnected: the ordinary convolution commutes with the Laplacian, and the law of Brownian motion has a convolution semigroup property with respect to the ordinary convolution. Seeking to generalize this useful connection, and also motivated by its probabilistic applications, the book focuses on the following question: given a diffusion process Xt on a metric space E, can we construct a convolution-like operator * on the space of probability measures on E with respect to which the law of Xt has the *-convolution semigroup property? A detailed analysis highlights the connection between the construction of convolution-like structures and disciplines such as stochastic processes, ordinary and partial differential equations, spectral theory, special functions and integral transforms. The book will be valuable for graduate students and researchers interested in the intersections between harmonic analysis, probability theory and differential equations.

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