Dependent Gaussian 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...

Complete convergence of moving-average processes under negative dependence sub-Gaussian assumptions

The complete convergence is investigated for moving-average processes of doubly infinite sequence of negative dependence sub-gaussian random variables with zero means, finite variances and absolutely summable coefficients. As a corollary, the rate of complete convergence is obtained under some suitable conditions on the coefficients.

Strong Convergence of Weighted Sums for Negatively Orthant Dependent Random Variables

We discuss in this paper the strong convergence for weighted sums of negatively orthant dependent (NOD) random variables by generalized Gaussian techniques. As a corollary, a Cesaro law of large numbers of i.i.d. random variables is extended in NOD setting by generalized Gaussian techniques.

ADK Entropy and ADK Entropy Rate in Irreducible- Aperiodic Markov Chain and Gaussian Processes

In this paper, the two parameter ADK entropy, as a generalized of Re'nyi entropy, is considered and some properties of it, are investigated. We will see that the ADK entropy for continuous random variables is invariant under a location and is not invariant under a scale transformation of the random variable. Furthermore, the joint ADK entropy, conditional ADK entropy, and chain rule of this ent...

Autoregressive Gaussian Random Vectors of First Order

Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations

We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes, by construction, are designed to deal with cases where: (1) all we observe are noisy data on black-box initial conditions, and (2) we are interested in quan...