2014/06/09 by Chuan-Zhong Chen, Li Ma, Chen, Chuan-Zhong +3
Mathematics · #31C25 #60J25 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:31C25 #msc:60J25
paper · pdf · doi:10.48550/arxiv.1406.2351
arxiv created 2014/06/09 · arxiv updated 2014/06/11
Let (E,D(E)) be a quasi-regular semi-Dirichlet form and (Xt)t≥0 be the associated Markov process. For u∈ D(E)loc, denote At[u]:=u(Xt)-u(X0) and F[u]t:=∑0<s≤ t( u(Xs)- u(Xs-))1_\| u(Xs)- u(Xs-)|>1\, where u is a quasi-continuous version of u. We show that there exist a unique locally square integrable martingale additive functional Y[u] and a unique continuous local additive functional Z[u] of zero quadratic variation such that At[u]=Yt[u]+Zt[u]+Ft[u]. Further, we define the stochastic integral ∫0t v(Xs-)dAs[u] for v∈ D(E)loc and derive the related Itô's formula.