A new approach to the skew product of symmetric Markov processes
弘之 大倉, Hiroyuki Ôkura · Institutional Repositories DataBase (IRDB) · 1998
The skew product of two independent symmetric Markov processes X^(1)_t and X^(2)_t is defined to be the process (X^(1)_t , X^(2)_A(t)) , where A(t) is a positive continuous additive functional of the first process. Both explicit formula and core of the Dirichlet form of the skew product process have been determined by Fukushima-Oshima 1) for conservative symmetric diffusion processes. This formula and the regularity of the Dirichlet form for conservative symmetric Markov processes have already been established by the present author 4) In the present paper, a simple proof of this formula will be given, along with detailed information on the core, for symmetric Markov processes which are not necessarily conservative. In the proof, Dirichlet forms perturbed by killing transformations are used, instead of the time change transformations used in previous research. Some results related to Fubini-type theorems and applications will also be given.