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Contents of PMS, Vol. 23, Fasc. 2,
pages 369 - 387
 

ON THE LOCAL TIME OF MULTIPARAMETER SYMMETRIC STABLE PROCESSES. REGULARITY AND LIMIT THEOREM IN BESOV SPACES

B. Boufoussi
M. Dozzi

Abstract: Let X = (X ,z  (-  T = [0,l]N)
      z     N be a symmetric a -stable process, 1 < a < 2. Based on a Kolmogorov type continuity theorem we show Hölder conditions in Lp  -norms for the local time of X 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.

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