78 research outputs found
Weak convergence to the tangent process of the linear multifractional stable motion
We also show that one can have degenerate tangent processes Z(t), when the function H(t) is not sufficiently regular. The LMSM process is closely related to the Gaussian multifractional Brownian motion (MBM) process. We establish similar weak convergence results for the MBM
Limit theorems for maxima of heavy-tailed terms with random dependent weights
We study the general case when the weights Wj , j N can be dependent and in particular long-range dependent. Under mild tail and convergence conditions on the weights Wjs, we establish limit theorems for scaled versions of the process fMn(t)gt_0, as n ! 1. The limit processes are mixtures of extremal Frechet processes. The results are valid when the laws of the Uj’s belong to the normal domain of attraction of a Frechet distribution or to a sub-class of the general domain of attraction of a Frechet law
Max-stable sketches: estimation of Lp-norms, dominance norms and point queries for non-negative signals
Max-stable random sketches can be computed efficiently on fast streaming
positive data sets by using only sequential access to the data. They can be
used to answer point and Lp-norm queries for the signal. There is an intriguing
connection between the so-called p-stable (or sum-stable) and the max-stable
sketches. Rigorous performance guarantees through error-probability estimates
are derived and the algorithmic implementation is discussed
- …