We prove sharp two-sided bounds of the fundamental solution for integro-differential operators of order α∈(0,2) that generate a d-dimensional Markov process. The corresponding Dirichlet form is comparable to that of d independent copies of one-dimensional jump processes, i.e., the jumping measure is singular with respect to the d-dimensional Lebesgue measure.
- Heat kernel
- Integro-differential operator
- Markov jump process
ASJC Scopus subject areas
- Applied Mathematics