Department of Mathematics

Probability

  •  Uniformly and Strongly Consistent Estimation for the Hurst Function of a Linear Multifrational Stable Motion
  •  04/13/2017
  •  3:00 PM - 3:50 PM
  •  C405 Wells Hall
  •  Antoine Ayache, University of Lille 1, France

Multifractional processes have been introduced in the 90's in order to overcome some limitations of the well-known Fractional Brownian Motion (FBM) due to the constancy in time of its Hurst parameter; in their context, this parameter becomes a Hölder continuous function. Global and local path roughness of a multifractional process are determined by values of this function; therefore, several authors have been interested in their statistical estimation, starting from discrete variations of the process. Because of the complex dependence structure of variations, showing consistency of estimators is a tricky problem which often requires hard computations. The main goal of our talk, is to introduce in the setting of the non-anticipative moving average Linear Multifractional Stable Motion (LMSM) with a stability parameter 'alpha' strictly larger than 1, a new strategy for dealing with the latter problem. In contrast with the previous strategies, this new one, does not require to look for sharp estimates of covariances related to variations; roughly speaking, it consists in expressing them in such a way that they become independent up to negligible remainders. This is a joint work with Julien Hamonier at University of Lille 2.

 

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