ON THE LOCAL TIME OF MULTIPARAMETER SYMMETRIC STABLE
PROCESSES. REGULARITY AND LIMIT THEOREM IN BESOV SPACES
Abstract: Let be a symmetric -stable process,
Based on a Kolmogorov type continuity theorem we show Hölder conditions in -norms
for the local time of with respect to the space and time variables, by distinguishing the
cases where the time variables do or do not meet the axes. Weak convergence of the
occupation integral is proved.
2000 AMS Mathematics Subject Classification: 60G17, 60G52, 60J55.
Key words and phrases: Local time, symmetric stable process, multiparameter process,
anisotropic Besov space, tightness, limit theorem.