Nonhomogeneous fractional integration and multifractional processes

Donatas Surgailis

Stochastic Processes and their Applications, 2008, vol. 118, issue 2, 171-198

Abstract: Extending the recent work of Philippe et al. [A. Philippe, D. Surgailis, M.-C. Viano, Invariance principle for a class of non stationary processes with long memory, C. R. Acad. Sci. Paris, Ser. 1. 342 (2006) 269-274; A. Philippe, D. Surgailis, M.-C. Viano, Time varying fractionally integrated processes with nonstationary long memory, Theory Probab. Appl. (2007) (in press)] on time-varying fractionally integrated operators and processes with discrete argument, we introduce nonhomogeneous generalizations I[alpha]([dot operator]) and D[alpha]([dot operator]) of the Liouville fractional integral and derivative operators, respectively, where , is a general function taking values in (0,1) and satisfying some regularity conditions. The proof of D[alpha]([dot operator])I[alpha]([dot operator])f=f relies on a surprising integral identity. We also discuss properties of multifractional generalizations of fractional Brownian motion defined as white noise integrals and s.

Keywords: Liouville; fractional; operators; Long-range; dependence; Multifractional; Brownian; motion; Nonhomogeneous; fractional; integration; Scaling; limits (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (7)

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