W. Vervaat (1985). Sample Path Properties of Self-similar Processes With Stationary Increments. Annals of Probability, 13:1--27. 79 Home/Search Document Not in Database Summary Related Articles Check |
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The Asymptotic Efficiency Of Simulation Estimators - Glynn, Whitt (1992) (8 citations) (Correct)
....rates also can arise in the estimation of steady state means as in Example 4.3 when there is long range dependence in the underlying stochastic process X. Instead of (16) a FCLT may hold with g 1 2. For examples of long range dependence, see Mandelbrot (1977) Taqqu (1982) Cox (1984) Vervaat (1985) and references cited there. 6. Supercanonical Estimator Convergence Rates In this section we give an example of an estimator having a supercanonical convergence rate. This estimator may have some intrinsic interest, but we present it primarily to illustrate how supercanonical convergence rates ....
VERVAAT, W. 1985. Sample path properties of self-similar processes with stationary increments. Ann. Probab. 13, 1-27.
An Introduction to the Theory of Selfsimilar Stochastic.. - Embrechts, Maejima (Correct)
.... = 1 2 t 2H s 2H jt sj 2H E jX(1)j 2 : Theorem 1.3 Let fX(t)g be nontrivial and H ss, si, H 0. i) Mae86] If E [jX(1)j ] 1 for some 1, then H 1= ii) If E[jX(1)j] 1, then H 1. iii) Kon84] If E[jX(1)j] 1 and 0 H 1, then E[X(t) 0. iv) [Ver85]) If E[jX(1)j] 1 and H = 1, then X(t) tX(1) a.s. ii) is easily seen from (i) Because of (ii) and (iv) above, when the process has nite rst moment, we always consider the case 0 H 1. Let fX(t) t 0g be nontrivial, H ss, si, 0 H 1, and E[jX(1)j 2 ] 1, and de ne (n) X(n ....
....2 . Sample path properties of Brownian motion have been well studied. As Brownian motion, fractional Brownian motion is also sample continuous, nowhere di erentiable and of unbounded variation almost surely. For sample path properties of general selfsimilar process with stationary increments, see [Ver85], and for that of selfsimilar stable processes with stationary increments, see [KonMae91] 6 Several properties of trajectories of multidimensional fractional Brownian motion with multiparameter have also been studied. Let fBH (t) t 2 R N g be a mean zero Gaussian process with covariance ....
W. Vervaat (1985) : Sample path properties of self-similar processes with stationary increments, Ann. Probab. 13, 1-27.
A Novel Approach to the Estimation of the Long-Range Dependence.. - Kettani (2002) (Correct)
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W. Vervaat (1985). Sample Path Properties of Self-similar Processes With Stationary Increments. Annals of Probability, 13:1--27. 79
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