From resolvents to càdlàg processes through compact excessive functions and applications to singular SDE on Hilbert spaces

doi:10.1016/j.bulsci.2011.07.002

Bulletin des Sciences Mathématiques

Volume 135, Issues 6–7, September–November 2011, Pages 844-870

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Abstract

We present an approach for constructing càdlàg strong Markov processes given a resolvent of kernels. The conditions imposed on the resolvent are checkable in applications and allow the control of the set of admissible starting points of the process. The main application is to singular SDEs on Hilbert spaces.

MSC

60J45

60J40

60J35

47D07

31C25

Keywords

Resolvent of kernels

Tight capacity

Lyapunov function

Right process

Càdlàg trajectories

Standard process

Singular SDE on Hilbert space