Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9495810 | Journal of Functional Analysis | 2005 | 46 Pages |
Abstract
We construct and analyze in a very general way time inhomogeneous (possibly also degenerate or reflected) diffusions in monotonely moving domains EâRÃRd, i.e. if Etâ{xâRd|(t,x)âE}, tâR, then either EsâEt, âs⩽t, or EsâEt, âs⩽t, s,tâR. Our major tool is a further developed L2(E,m)-analysis with well chosen reference measure m. Among few examples of completely different kinds, such as e.g. singular diffusions with reflection on moving Lipschitz domains in Rd, non-conservative and exponential time scale diffusions, degenerate time inhomogeneous diffusions, we present an application to what we name skew Bessel process on γ. Here γ is either a monotonic function or a continuous Sobolev function. These diffusions form a natural generalization of the classical Bessel processes and skew Brownian motions, where the local time refers to the constant function γâ¡0.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Francesco Russo, Gerald Trutnau,