The Kalman-Bucy method is here analized and applied to the solution of a specific filtering problem to increase the signal message/noise ratio. The method is a time domain treatment of a geophysical process classified as stochastic non-stationary. The derivation of the estimator is based on the relationship between the Kalman-Bucy and Wiener approaches for linear systems. In the present work we...

The thesis is devoted to the study of solutions to the following linear recursion: Xn+1 = γXn + ξn, where γ ∈ (0, 1) is a constant and (ξn)n∈Z is a stationary and ergodic sequence of normal variables with random means and variances. More precisely, we assume that ξn = μn + σnεn, where (ε)n∈Z is an i.i.d. sequence of standard normal variables and (μn, σn)n∈Z is a stationary and ergodic process i...

If A is a nite alphabet, U Z D , and U is a probability measure on A U that \looks like" the marginal projection of a stationary stochas-tic process on A Z D , then can we \extend" U to such a process? Under what conditions can we make this extension ergodic, (quasi)periodic, or (weakly) mixing? After surveying classical work on this problem when D = 1, we provide some suucient conditions and s...

We study the stationary solution to the recursion Xn+1 = γXn+ξn, where γ ∈ (0, 1) is a constant and ξn are Gaussian variables with random parameters. Specifically, we assume that ξn = μn + σnεn, where (ε)n∈Z is an i.i.d. sequence of standard normal variables and (μn, σn)n∈Z is a stationary and ergodic process independent of (εn)n∈Z, which serves as an exogenous dynamic environment for the model...

The present work investigates two properties of level crossings of a stationary Gaussian process X(t) with autocorrelation function RX(τ). We show firstly that if RX(τ) admits finite second and fourth derivatives at the origin, the length of up-excursions above a large negative level −γ is asymptotically exponential as −γ → −∞. Secondly, assuming that RX(τ) admits a finite second derivative at ...

The FNSGP algorithm for Gaussian process model is proposed in this paper. It reduces the time cost to accelerate the task of non-stationary time series prediction without loss of accuracy. Some experiments are verified on the real world power load data.

Persistent oscillations are a common problem in process plants since they cause excessive variation in process variables and may compromise the product quality. This paper proposes a method for detecting oscillations in non-stationary time series. The method is based on the statistical properties of zero-crossings and it removes the non-stationary trend component from a signal before applying a...

If A is a finite alphabet, U ⊂ Z, and μU is a probability measure on A that “looks like” the marginal projection of a stationary stochastic process on A D , then can we “extend” μU to such a process? Under what conditions can we make this extension ergodic, (quasi)periodic, or (weakly) mixing? After surveying classical work on this problem when D = 1, we provide some sufficient conditions and s...

We introduce a stochastic process that describes a finite-velocity damped motion on the real line. Differently from the telegraph process, the random times between consecutive velocity changes have exponential distribution with linearly increasing parameters. We obtain the probability law of the motion, which admits a logistic stationary limit in a special case. Various results on the distribut...

Long been observed characteristics of empirical VBR process is its slowly decaying sample autocorrelations. In this work, we explain slowly decaying sample autocorrelations of the empirical VBR using the non-stationary model, which well reflects the stochastic characteristics of VBR process. Our model generates the synthetic sequence which has the same periodic characteristics as well as slowly...