On a certain class of semigroups of operators

2010/10/28 by Paolo Aniello, Aniello, Paolo
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #advanced mathematical theories #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1010.5925

11 pages

openalex publication_date 2010/10/28 · arxiv created 2010/10/29 · arxiv updated 2010/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define an interesting class of semigroups of operators in Banach spaces, namely, the randomly generated semigroups. This class contains as a remarkable subclass a special type of quantum dynamical semigroups introduced by Kossakowski in the early 1970s. Each randomly generated semigroup is associated, in a natural way, with a pair formed by a representation or an antirepresentation of a locally compact group in a Banach space and by a convolution semigroup of probability measures on this group. Examples of randomly generated semigroups having important applications in physics are briefly illustrated.

Citations

• Dynamical Theories of Brownian Motion

Related

• Law of Large Numbers for Random Quantum Dynamical Semigroups
• Stochastic Properties of Dynamical Systems Arising from (quantum) Spaces and Actions of Groups
• Playing with functions of positive type, classical and quantum
• Quantum Stochastic Calculus and Quantum Gaussian Processes
• The Strong Law of Large Numbers for random semigroups on uniformly smooth Banach spaces