2013/03/14 by Wei Sun, Jing Zhang, Sun, Wei +1
Economics, Econometrics and Finance · Mathematics · #31C25 #60J25 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #advanced mathematical theories #math.PR #msc:31C25 #msc:60J25
paper · pdf · doi:10.48550/arxiv.1303.3552
openalex publication_date 2013/03/14 · arxiv created 2013/04/11 · arxiv updated 2013/04/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let U be an open set of ℝn, m a positive Radon measure on U such that \rm supp[m]=U, and (Pt)t>0 a strongly continuous contraction sub-Markovian semigroup on L2(U;m). We investigate the structure of (Pt)t>0. (i) Denote respectively by (A,D(A)) and ( A,D( A)) the generator and the co-generator of (Pt)t>0. Under the assumption that C∞0(U)⊂ D(A)∩ D( A), we give an explicit Lévy-Khintchine type representation of A on C∞0(U). (ii) If (Pt)t>0 is an analytic semigroup and hence is associated with a semi-Dirichlet form (\cal E, D(\cal E)), we give an explicit characterization of \cal E on C∞0(U) under the assumption that C∞0(U)⊂ D(\cal E). We also present a LeJan type transformation rule for the diffusion part of regular semi-Dirichlet forms on general state spaces.