Abstract
We consider random walks and Lévy processes in a homogeneous group G. For all p>0, we completely characterise (almost) all Gvalued Lévy processes whose sample paths have finite pvariation, and give sufficient conditions under which a sequence of Gvalued random walks converges in law to a Lévy process in pvariation topology. In the case that G is the free nilpotent Lie group over Rd, so that processes of finite pvariation are identified with rough paths, we demonstrate applications of our results to weak convergence of stochastic flows and provide a LévyKhintchine formula for the characteristic function of the signature of a Lévy process. At the heart of our analysis is a criterion for tightness of pvariation for a collection of càdlàg strong Markov processes.
Original language  English 

Pages (fromto)  891932 
Number of pages  42 
Journal  Probability theory and related fields 
Volume  170 
Issue number  34 
DOIs  
Publication status  Published  17 May 2017 
Fingerprint
Dive into the research topics of 'Random walks and Lévy processes as rough paths'. Together they form a unique fingerprint.Profiles

Ilya Chevyrev
 School of Mathematics  Reader in Probability and Stochastic Analysis
Person: Academic: Research Active (Teaching)