We work on the statistical inference for several classes of stochastic processes.

Long memory processes are stationary processes whose  the autocorrelation function exhibits persistence. , They  play an important  role in fields as diverse as econometry, finance, hydrology, physical sciences…   We study long memory processes  to understand probabilistic foundations and statistical principles.

The aggregation  provides a class of  models for which we  propose new techniques of estimation. We also build testing procedures for detecting the presence of long memory in time series or for comparing the intensity of the memory of two time series.

Self-regulating processes are stochastic processes whose the pointwise Hölder exponent is a function of amplitude. We propose an estimator of  this function  using non parametric approach.  Asymptotic properties validate our inference method.

The  multistable processes  generalize stable processes  in the sense that the intensity of jumps varies in time.  We study the problem of discriminate between stable and multistable processes.

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