A Necessary Characteristic Equation of Diffusion Processes Having Gaussian Marginals

A Family of Non-Gaussian Martingales with Gaussian Marginals

We construct a family of martingales with Gaussian marginal distributions. We give a weak construction as Markov, inhomogeneous in time processes, and compute their infinitesimal generators. We give the predictable quadratic variation and show that the paths are not continuous. The construction uses distributions Gσ having a logconvolution semigroup property. Further, we categorize these proces...

Diffusion Equation and Stochastic Processes.

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...

On Gaussian Marginals of Uniformly Convex Bodies

We show that many uniformly convex bodies have Gaussian marginals in most directions in a strong sense, which takes into account the tails of the distributions. These include uniformly convex bodies with power type 2, and power type p > 2 with some additional type condition. In particular, all unit-balls of subspaces of Lp for 1 < p < ∞ have Gaussian marginals in this strong sense. Using the we...

Contrastive Divergence In Gaussian Diffusion Processes

Contrastive Divergence (CD) is a recent learning rule found to work very well in practice despite its still unclear theoretical underpinnings (Carreira-Perpiñan and Hinton, 2005; Hinton, 2002; Hinton and Salakhutdinov, 2006; Hyvärinen, 2006; MacKay, 2001; Roth and Black, 2005; Williams and Agakov, 2002; Yuille, 2004). This paper presents a theoretical analysis of CD in Gaussian Diffusion Proces...