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- W1991758809 abstract "Abstract The purpose of this paper is to prove a Kolmogorov and a tightness criterion in a class of modular Besov spaces that present a natural extension of the work in [8] Boufoussi , B. , and Lakhel , E. 2001 . Weak convergence in Besov spaces to fractional Brownian motion . C. R. Acad. Sci. Paris, Série I 333 : 39 – 44 .[Crossref] , [Google Scholar]. We apply these criteria to establish regularity results and weak approximations in these spaces for a class of Gaussian processes, which admit integral representations of the form where (W t , t ∈ [0, 1]) is a standard Brownian motion and K is a kernel satisfying suitable regularity properties. The most classical example of these processes is the fractional Brownian motion. The case of the multifractional Brownian motion is considered. These approximation results are a refinement of those of Stroock [21] Stroock , D. W. 1982 . Tata Institute of Fundamental Research Topics in Stochastic Differential Equations . Berlin : Springer . [Google Scholar] and Delgado and Jolis [13] Delgado , R. , and M. Jolis 2000 . Weak approximation for a class of Gaussian processes . J. Appl. Prob. 37 : 400 – 407 . [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar] who considered the cases of Brownian motion and fractional Brownian motion in the space of continuous functions." @default.
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- W1991758809 date "2005-07-01" @default.
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- W1991758809 title "A Kolmogorov and Tightness Criterion in Modular Besov Spaces and an Application to a Class of Gaussian Processes" @default.
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