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- W175800541 abstract "We consider chaos expansion in generalized random variable spaces exp(S)‰;H and exp(S)i‰;H based on fractional white noise space, which correspond to the ones studied in (6). Generalized stochastic pro- cesses with values in these spaces are proven to have a series expansion, and difierent Wick products are discussed. In this paper we develop a version of chaos expansion theorems in spaces of generalized random variables of Kondratiev type, expansion of generalized random processes, and the Wick product. Our study will be based on fractional white noise spaces; for a detailed review of fractional white noise theory we refer to (1), (2) and (4). Since there exists an isomorphism between the classical white noise space and the fractional white noise space, all theorems stated in this paper can be proven verbatim as in (6); one just has to replace the orthogonal basis of the space of generalized random variables with the orthogonal basis of the corresponding fractional versions of these spaces. Also, we consider the general case ‰ 2 (0;1), while in (6) we studied the case ‰ = 1; H = 1 . We recall some basic deflnitions from (3), (4), (5) and (7). 1.1. Fractional Brownian motion on white noise spaces Deflnition 1.1. Fractional Brownian motion (fBm) with Hurst index H 2 (0;1) is a Gaussian process B (H) = fB (H) t (¢); t 2 Rg on (›;F;), with B (H) 0 = 0; zero expectation E(B (H) t ) = 0 for all t 2R; and covariance function" @default.
- W175800541 created "2016-06-24" @default.
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- W175800541 date "2008-01-01" @default.
- W175800541 modified "2023-09-27" @default.
- W175800541 title "CHAOS EXPANSION OF GENERALIZED RANDOM PROCESSES ON FRACTIONAL WHITE NOISE" @default.
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