BOX DIMENSION OF INTERPOLATIONS OF SELF-SIMILAR PROCESSES
WITH STATIONARY INCREMENTS
Abstract: We prove that under a general condition interpolation dimensions of
-sssi process converge in probability to The result can be applied to a wide class
of -sssi processes which includes fractional Brownian motions, -fractional
stable processes or strictly stable -sssi processes. Moreover, we prove that for an
-sssi process with continuous sample paths the same general condition implies uniform
convergence in probability of sample paths of fractal interpolations to sample paths of the
interpolated process.
1991 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: Fractal interpolation, interpolation dimension, box dimension,
self-similar process, stationary increments, stable process.