2020/06/24 by Sergio Albeverio, Toshinao Kagawa, Albeverio, Sergio +5 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #(2020)31C25 #46E27 #46N30 #46N50 #47D07 #60H15 #60J46 #60J75 #81S20 #Bayesian Methods and Mixture Models #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories #math.FA #math.PR #msc:46E27 #msc:46N30 #msc:46N50 #msc:47D07 #msc:60H15 #msc:60J46 #msc:60J75 #msc:81S20
paper · pdf · doi:10.48550/arxiv.2006.13571
openalex publication_date 2020/06/24 · arxiv created 2021/09/21 · arxiv updated 2021/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
General theorems on the closability and quasi-regularity of non-local Markovian symmetric forms on probability spaces (S, \cal B(S), μ), with S Fréchet spaces such that S ⊂ \mathbb R\mathbb N, \cal B(S) is the Borel σ-field of S, and μ is a Borel probability measure on S, are introduced. Firstly, a family of non-local Markovian symmetric forms \cal E(α), 0 < α< 2, acting in each given L2(S; μ) is defined, the index α characterizing the order of the non-locality. Then, it is shown that all the forms \cal E(α) defined on \bigcup_n ∈ \mathbb N C∞0(\mathbb Rn) are closable in L2(S;μ). Moreover, sufficient conditions under which the closure of the closable forms, that are Dirichlet forms, become strictly quasi-regular, are given. Finally, an existence theorem for Hunt processes properly associated to the Dirichlet forms is given. The application of the above theorems to the problem of stochastic quantizations of Euclidean Φ4d fields, for d =2, 3, by means of these Hunt processes is indicated.