作者：Morvai, Gusztav; Weiss, Benjamin
作者单位：MTA-BME Stochastics Research Group; Hebrew University of Jerusalem
摘要：We study the problem of finding an universal estimation scheme h(n) : R(n) -> R, n = 1, 2,... which will satisfy limt(->infinity) l/t Sigma(t)(i=1)|h(i)(X(0), X(1)....,X(i-l)) -E(X(i)|X(0), X(1),....,X(i-1))|(p) = 0 a.s. for all real valued stationary and ergodic processes that are in L. We will construct a single such scheme for all 1 < p <= infinity, and show that for p = 1 mere integrability does not suffice but L log(+) L does.
作者：Nualart, David; Tindel, Samy
作者单位：University of Kansas; Universite de Lorraine
摘要：This note is devoted to construct a rough path above a multidimensional fractional Brownian motion B with any Hurst parameter H is an element of (0, 1), by means of its representation as a Volterra Gaussian process. This approach yields some algebraic and computational simplifications with respect to [Stochastic Process. Appl. 120 (2010) 1444-1472], where the construction of a rough path over B was first introduced.
