Some comments on spectral representations of non-stationary stochastic processes

1973 ◽  
Vol 10 (04) ◽  
pp. 881-885 ◽  
Author(s):  
H. Tong
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Stationary Stochastic Process ◽  
Sufficient Condition ◽  
Stationary Stochastic Processes ◽  
Spectral Representations ◽  
Oscillatory Processes

The first part of the paper gives a multitude of essentially different representations of a stationary stochastic process. The second part gives a sufficient condition for the sum of two oscillatory processes to be again oscillatory.

Some comments on spectral representations of non-stationary stochastic processes

1973 ◽  
Vol 10 (4) ◽  
pp. 881-885 ◽  
Author(s):  
H. Tong
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Stationary Stochastic Process ◽  
Sufficient Condition ◽  
Stationary Stochastic Processes ◽  
Spectral Representations ◽  
Oscillatory Processes

The first part of the paper gives a multitude of essentially different representations of a stationary stochastic process. The second part gives a sufficient condition for the sum of two oscillatory processes to be again oscillatory.

Representation of Strongly Stationary Stochastic Processes

1993 ◽  
Vol 60 (3) ◽  
pp. 689-694 ◽  
Author(s):  
M. Di Paola
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Linear Systems ◽  
Stationary Processes ◽  
Orthogonality Conditions ◽  
Probabilistic Characterization ◽  
Stationary Stochastic Processes ◽  
Fixed Order ◽  
Strongly Stationary

A generalization of the orthogonality conditions for a stochastic process to represent strongly stationary processes up to a fixed order is presented. The particular case of non-normal delta correlated processes, and the probabilistic characterization of linear systems subjected to strongly stationary stochastic processes are also discussed.

scholarly journals Univariate Conditional Distributions of an Open-Loop TAR Stochastic Process

2016 ◽  
Vol 39 (2) ◽  
pp. 149
Author(s):  
Fabio Nieto ◽  
Edna C. Moreno
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Open Loop ◽  
Conditional Variance ◽  
Sufficient Condition ◽  
Conditional Distributions ◽  
Threshold Autoregressive ◽  
Sample Paths ◽  
Weak Stationarity ◽  
Stochastic Mechanism

<p>Clusters of large values are observed in sample paths of certain open-loop threshold autoregressive (TAR) stochastic processes. In order to characterize the stochastic mechanism that generates this empirical stylized fact, three types of marginal conditional distributions of the underlying stochastic process are analyzed in this paper. One allows us to find the conditional variance function that explains the aforementioned stylized fact. As a by-product, we are able to derive a sufficient condition to have asymptotic weak stationarity in an open-loop TAR stochastic process.</p>

Analysis and Probabilistic Modeling of the Stationary Ice Loads Stochastic Process With Lognormal Distribution

2014 ◽  
Author(s):  
Petr Zvyagin ◽  
Kirill Sazonov
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Normal Distribution ◽  
Autocorrelation Function ◽  
Strain Gauge ◽  
Lognormal Distribution ◽  
Probabilistic Modeling ◽  
Stationary Stochastic Process ◽  
Strain Gauge Transducer ◽  
Ice Loads

Until recent times researchers who investigated ice loads stochastic processes usually stated the fact of normal distribution for them. In the paper the model of a stationary stochastic process with a lognormal distribution for ice loads is offered. This model relates to the strain gauge transducer ice loads measurements as well as to some examples considered in different papers that were published earlier. For this model dependencies of the autocorrelation function were found that allows to simulate the ice loads process relatively easily. The procedure of such a simulation is described in details and the example of the analysis and simulation ice loads measurements is provided.

Multiple images of stochastic processes

1983 ◽  
Vol 94 (1) ◽  
pp. 183-188
Author(s):  
Simeon M. Berman
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Lebesgue Measure ◽  
Random Fields ◽  
Positive Lebesgue Measure ◽  
Sufficient Condition ◽  
Large Classes ◽  
Multiple Images ◽  
Simple Sufficient Condition

AbstractA simple sufficient condition is given for a stochastic process x(t), 0 ≤ t ≤ 1, to have the following property: There is an integer m ≥ 2 such that for any non-degenerate subinterval J ⊂ [0, 1], there exist m disjoint subintervals I1, …, Im ⊂ J such that the intersection of the images of I1,…, Im under the mapping by x(·) has positive Lebesgue measure, almost surely. There is also a version for vector random fields; and the main result is shown to apply to large classes of processes.

scholarly journals Linear rigidity of stationary stochastic processes

2017 ◽  
Vol 38 (7) ◽  
pp. 2493-2507 ◽  
Author(s):  
ALEXANDER I. BUFETOV ◽  
YOANN DABROWSKI ◽  
YANQI QIU
Keyword(s):  
Stochastic Processes ◽  
Point Processes ◽  
Linear Span ◽  
Sufficient Condition ◽  
Determinantal Point Processes ◽  
Determinantal Point Process ◽  
Zygmund Class ◽  
Closed Linear Span ◽  
Stationary Stochastic Processes ◽  
Tensor Square

We consider stationary stochastic processes $\{X_{n}:n\in \mathbb{Z}\}$ such that $X_{0}$ lies in the closed linear span of $\{X_{n}:n\neq 0\}$; following Ghosh and Peres, we call such processes linearly rigid. Using a criterion of Kolmogorov, we show that it suffices, for a stationary stochastic process to be linearly rigid, that the spectral density vanishes at zero and belongs to the Zygmund class $\unicode[STIX]{x1D6EC}_{\ast }(1)$. We next give a sufficient condition for stationary determinantal point processes on $\mathbb{Z}$ and on $\mathbb{R}$ to be linearly rigid. Finally, we show that the determinantal point process on $\mathbb{R}^{2}$ induced by a tensor square of Dyson sine kernels is not linearly rigid.

scholarly journals Stochastic Processes with a Particular Type of Variograms

2007 ◽  
Vol 2007 ◽  
pp. 1-5 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Stochastic Processes ◽  
Series Expansion ◽  
Real Line ◽  
Random Fields ◽  
The Other ◽  
Simple Construction ◽  
The Real ◽  
Line Form

This paper is concerned with a class of stochastic processes or random fields with second-order increments, whose variograms have a particular form, among which stochastic processes having orthogonal increments on the real line form an important subclass. A natural issue, how big this subclass is, has not been explicitly addressed in the literature. As a solution, this paper characterizes a stochastic process having orthogonal increments on the real line in terms of its variogram or its construction. Our findings are a little bit surprising: this subclass is big in terms of the variogram, and on the other hand, it is relatively “small” according to a simple construction. In particular, every such process with Gaussian increments can be simply constructed from Brownian motion. Using the characterizations we obtain a series expansion of the stochastic process with orthogonal increments.

scholarly journals A discrete Stochastic Korovkin theorem

1991 ◽  
Vol 14 (4) ◽  
pp. 679-682
Author(s):  
George A. Anastassiou
Keyword(s):  
Stochastic Processes ◽  
State Space ◽  
Sufficient Condition ◽  
Korovkin Theorem ◽  
Index Set ◽  
Real State

In this article we give a sufficient condition for the pointwise−−in the first mean Korovkin property onB0(P), the space of stochastic processes with real state space and countable index setΓand bounded first moments.

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