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Growth and Hölder conditions for the sample paths of Feller processes
journal contribution
posted on 2023-06-08, 00:11 authored by Rene SchillingLet (A,D(A)) be the infinitesimal generator of a Feller semigroup such that C c 8(R n )?D(A) and A|C c 8(R n ) is a pseudo-differential operator with symbol -p(x,?) satisfying |p(•,?)|8=c(1+|?|2) and |Imp(x,?)|=c 0Rep(x,?). We show that the associated Feller process {X t } t =0 on R n is a semimartingale, even a homogeneous diffusion with jumps (in the sense of [21]), and characterize the limiting behaviour of its trajectories as t?0 and 8. To this end, we introduce various indices, e.g., ß8 x :={?>0:lim |?|?8 | x - y |=2/|?||p(y,?)|/|?|?=0} or d8 x :={?>0:liminf |?|?8 | x - y |=2/|?| |e|=1|p(y,|?|e)|/|?|?=0}, and obtain a.s. (P x ) that lim t ?0 t -1/? s = t |X s -x|=0 or 8 according to ?>ß8 x or ?
History
Publication status
- Published
Journal
Probability Theory and Related FieldsISSN
0178-8051Publisher
Springer VerlagExternal DOI
Issue
4Volume
112Page range
565-611ISBN
0178-8051Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
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2012-02-06Usage metrics
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