Financial models consider often stochastic processes satisfying certain differential equations. We show that the solution of a particular geometric Brownian motion observed in discrete time is asymptotically equivalent with a Gaussian white noise model.

We give here a simulation study of a density estimator, issued from sharp adaptive estimation. This nonparametric estimator was previously proved to have interesting theoretical properties. In this paper we describe the method and apply it successfully to i.i.d. simulated data issued from...

We give here a simulation study of a density estimator, issued from sharp adaptive estimation. This nonparametric estimator was previously proved to have interesting theoretical properties. In this paper we describe the method and apply it successfully to i.i.d. simulated data issued from...

Financial models consider often stochastic processes satisfying certain differential equations. We show that the solution of a particular geometric Brownian motion observed in discrete time is asymptotically equivalent with a Gaussian white noise model.

We consider copulas with a given diagonal section and compute the explicit density of the unique optimal copula which maximizes the entropy. In this sense, this copula is the least informative among the copulas with a given diagonal section. We give an explicit criterion on the diagonal section...

We estimate the common density function of n i.i.d. observations, at a fixed point, over Sobolev classes of functions having regularity [beta]. We prove that the optimal rate of convergence cannot be attained in adaptive estimation, i.e. uniformly over [beta] in some interval Bn. A slower rate...

type="main" xml:id="sjos12015-abs-0001" <title type="main">ABSTRACT</title>We consider in this paper the semiparametric mixture of two unknown distributions equal up to a location parameter. The model is said to be semiparametric in the sense that the mixed distribution is not supposed to belong to a parametric family. To...

We consider the problem of mixing k random variables where each of the k components results from shifting a common random variable X0 with a certain probability. We show that if X0 admits a density that is a Pólya frequency function with E[X0]=0, then k, a1,…,ak and π1,…,πk are...