Stochastic processes as Fourier transforms of stochastic measures

Stochastic Processes as Fourier Integrals and Dilation of Vector Measures

Smoothing and occupation measures of stochastic processes

This is a review paper about some problems of statistical inference for one-parameter stochastic processes, mainly based upon the observation of a convolution of the path with a non-random kernel. Most of the results are known and presented without proofs. The tools are first and second order approximation theorems of the occupation measure of the path, by means of functionals defined on the sm...

Fourier Transforms of Stationary Processes

We consider the asymptotic behavior of Fourier transforms of stationary and ergodic sequences. Under sufficiently mild conditions, central limit theorems are established for almost all frequencies as well as for a given frequency. Applications to the widely used linear processes and iterated random functions are discussed. Our results shed new light on the foundation of spectral analysis in tha...

The new maximal measures for stochastic processes

In recent work the author proposed a reformed notion of stochastic processes, which in particular removes notorious problems with uncountable time domains. In case of a Polish state space the new stochastic processes are in one-to-one correspondence with the traditional ones. This implies for a stochastic process that the traditional canonical measure on the path space receives a certain distin...

Surface Measures - Maximal Functions and Fourier Transforms