We consider a multivariate Langevin equation in discrete time, driven by a force induced by certain Gibbs' states. The main goal of the paper is to study the asymptotic behavior of a random walk with stationary increments (which are interpreted as discrete-time speed terms) satisfying the Langevin equation. We observe that (stable) functional limit theorems and laws of iterated logarithm for re...

This paper proposes to use the method of generalized empirical likelihood to find the optimal portfolio weights. The log-returns of assets are modeled by multivariate stationary processes rather than i.i.d. sequences. The variance of the portfolio is written by the spectral density matrix, and we seek the portfolio weights which minimize it.

We consider the optimal transport problem between multivariate Gaussian stationary stochastic processes. The transportation effort is variance of filtered discrepancy process. main contribution this article to show that corresponding solution leads a weighted Hellinger distance power spectral densities. Then, we propose estimation approach in case indirect measurements, which based on distance.

We are going to give necessary and sufficient conditions for a multivari-ate stationary stochastic process to be completely regular. We also give the answer to a question of V.V. Peller concerning the spectral measure characterization of such processes.

For a multivariate stationary process, we develop explicit representations for the finite predictor coefficient matrices, the finite prediction error covariance matrices and the partial autocorrelation function (PACF) in terms of the Fourier coefficients of its phase function in the spectral domain. The derivation is based on a novel alternating projection technique and the use of the forward a...

comNode classification within Membrane Residue Curves (M-RCMs) currently hinges on Lyapunov’s Theorem and therefore the computation of mathematically complex eigenvalues. This paper presents an alternative criterion for the classification of nodes within M-RCMs based on the total membrane flux at node compositions. This paper demonstrates that for a system exhibiting simple permeation behaviour...

We investigate transition law between consecutive observations of Ornstein-Uhlenbeck processes of infinite variation with tempered stable stationary distribution. Thanks to the Markov autoregressive structure, the transition law can be written in the exact sense as a convolution of three random components; a compound Poisson distribution and two independent tempered stable distributions, one wi...

Multivariate time series exhibit two types of dependence: across variables and points. Vine copulas are graphical models for the dependence can conveniently capture both in same model. We derive maximal class graph structures that guarantee stationarity under a natural verifiable condition called translation invariance. propose computationally efficient methods estimation, simulation, predictio...