We study the ergodic properties of finite-dimensional systems of SDEs driven by non-degenerate additive fractional Brownian motion with arbitrary Hurst parameter H ∈ (0, 1). A general framework is constructed to make precise the notions of “invariant measure” and “stationary state” for such a system. We then prove under rather weak dissipativity conditions that such an SDE possesses a unique st...

We propose the entropy of random Markov trajectories originating and terminating at a state as a measure of the stability of a state of a Markov process. These entropies can be computed in terms of the entropy rates and stationary distributions of Markov processes. We apply this definition of stability to local maxima and minima of the stationary distribution of the Moran process with mutation ...

We study the totally asymmetric exclusion process on the positive integers with a single particle source at the origin. Liggett (1975) has shown that the long term behaviour of this process has a phase transition: If the particle production rate at the source is below a critical value, the stationary measure is a product measure, otherwise the stationary measure is spatially correlated. Followi...

Voice activity detection is an essential part of many speech processing algorithms. The requirements of the speech application determine the design of voice activity detection. Some applications need low-latency results whereas the accuracy of speech detection is more important for other applications. The performance is generally evaluated by Receiver Operating Characteristic (ROC) curves, whic...

We show that Zhang’s sandpile model (N , [a, b]) on N sites and with uniform additions on [a, b] has a unique stationary measure for all 0 ≤ a < b ≤ 1. This generalizes earlier results of [6] where this was shown in some special cases. We define the infinite volume Zhang’s sandpile model in dimension d ≥ 1, in which topplings occur according to a Markov toppling process, and we study the stabil...

Non-stationary effects are ubiquitous in real world data. In many settings, the observed signals are a mixture of underlying stationary and non-stationary sources that cannot be measured directly. For example, in EEG analysis, electrodes on the scalp record the activity from several sources located inside the brain, which one could only measure invasively. Discerning stationary and non-stationa...

in recent years there has been considerable interest in the synthesis and separation of enantiomers of organic compounds especially because of their importance in the biochemistry and pharmaceutical industry. high-performance liquid chromatography is a very useful method for the direct separation of enantiomers. however, about 30−40 years ago, commercially available chiral stationary phases wer...

in analyzing a signal, especially a non-stationary signal, it is often necessarythe desired signal to be segmented into small epochs. segmentation can beperformed by splitting the signal at time instances where signal amplitude orfrequency change. in this paper, the signal is initially decomposed into signals withdifferent frequency bands using wavelet transform. then, fractal dimension of thed...

We study the invariant measure or the stationary density of a coupled discrete dynamical system as a function of the coupling parameter ǫ (0 < ǫ < 1/4). The dynamical system considered is chaotic and unsynchronized for this range of parameter values. We find that the stationary density, restricted on the synchronization manifold, is a fractal function. We find the lower bound on the fractal dim...

We study stationary measures for the two-dimensional Navier-Stokes equation with periodic boundary condition and random forcing. We prove uniqueness of the stationary measure under the condition that all “determining modes” are forced. The main idea behind the proof is to study the Gibbsian dynamics of the low modes obtained by representing the high modes as functionals of the time-history of t...