Multidimensional IFRA Processes

Multidimensional random processes with normal covariances

where R(*) is a weakly stationary covariance. Thanks to the facts that R(s, s) ^ 0 for every seU1 and R (0) ^ 0 this definition yields R(s) !> 0 for every s e (R__. The definition of local stationarity for random sequences is given in [4]. In this case a covariance function R(-, •), defined on Z x Z (Cartesian product of integers), can be expressed as R(n, m) = R(n + m) R(n m) where R(*) is a s...

Singular ergodic control for multidimensional Gaussian processes

Multidimensional Wick-itô Formula for Gaussian Processes

Detecting change-points in multidimensional stochastic processes

Ageneral test statistic for detecting change-points inmultidimensional stochastic processes with unknown parameters is proposed. The test statistic is specialized to the case of detecting changes in sequences of covariance matrices. Large-sample distributional results are presented for the test statistic under the null hypothesis of no-change. The finite-sample properties of the test statistic ...

Limit Theorems for Multidimensional Markov Processes

An informal exposition of some recent results and conjectures. A multidimensional Markov process (mdmp) is a dynamical system (K, m, T) where: K space of the sequences of symbols from a finite alphabet / = (α, fo,... z) indexed by the elements η e Z = lattice formed by the d-ples of integers. K is regarded as K = TίηeZd I i.e. as a product space of copies of/; furthermore / is topologized by th...