Conjunction Probability of Smooth Centered Gaussian Processes

Small Deviations of Smooth Stationary Gaussian Processes

We investigate the small deviation probabilities of a class of very smooth stationary Gaussian processes playing an important role in Bayesian statistical inference. Our calculations are based on the appropriate modification of the entropy method due to Kuelbs, Li, and Linde as well as on classical results about the entropy of classes of analytic functions. They also involve Tsirelson’s upper b...

Probability HITTING TIMES FOR GAUSSIAN PROCESSES

Modelling Smooth Paths Using Gaussian Processes

A generative model based on the gaussian mixture model and gaussian processes is presented in this paper. Typical motion paths are learnt and then used for motion prediction using this model. The principal novel aspect of this approach is the modelling of paths using gaussian processes. It allows the representation of smooth trajectories and avoids discretization problems found in most existing...

The Rate of Entropy for Gaussian Processes

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

Small deviations for a family of smooth Gaussian processes

We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling properties as standard Brownian motion and plays an important role in the study of zeros of random polynomials. Our estimates are based on several approaches. The precise result for the L2-norm is obtained by an appropriate modificatio...