scholarly journals Alternative estimate of curve exceeding probability of sub-Gaussian random process

2020 ◽  
pp. 37-39
Author(s):  
O. Kollie ◽  
R. Yamnenko
Keyword(s):  
Stochastic Process ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Special Interest ◽  
Queuing Theory ◽  
Random Processes ◽  
Financial Mathematics ◽  
Continuous Linear ◽  
Gaussian Random Process ◽  
Overflow Probability

Investigation of sub-gaussian random processes are of special interest since obtained results can be applied to Gaussian processes. In this article the properties of trajectories of a sub-Gaussian process drifted by a curve a studied. The following functionals of extremal type from stochastic process are studied: $\sup_{t\in B}(X(t)-f(t))$, $\inf{t\in B}(X(t)-f(t))$ and $\sup_{t\in B}|X(t)-f(t)|$. An alternative estimate of exceeding by sub-Gaussian process a level, given by a continuous linear curve is obtained. The research is based on the results obtained in the work \cite{yamnenko_vasylyk_TSP_2007}. The results can be applied to such problems of queuing theory and financial mathematics as an estimation of buffer overflow probability and bankruptcy

Extreme values of the cyclostationary Gaussian random process

1993 ◽  
Vol 30 (01) ◽  
pp. 82-97 ◽  
Author(s):  
D. G. Konstant ◽  
V.I. Piterbarg
Keyword(s):  
Gaussian Process ◽  
Random Process ◽  
Gaussian Processes ◽  
Extreme Values ◽  
Random Processes ◽  
Mean Square ◽  
Gaussian Random Process ◽  
Covariance Functions ◽  
Limit Formula ◽  
Image Position

In this paper the class of cyclostationary Gaussian random processes is studied. Basic asymptotics are given for the class of Gaussian processes that are centered and differentiable in mean square. Then, under certain conditions on the non-degeneration of the centered cyclostationary Gaussian process with integrable covariance functions, the Gnedenko-type limit formula is established for and all x > 0.

Extreme values of the cyclostationary Gaussian random process

1993 ◽  
Vol 30 (1) ◽  
pp. 82-97 ◽  
Author(s):  
D. G. Konstant ◽  
V.I. Piterbarg
Keyword(s):  
Gaussian Process ◽  
Random Process ◽  
Gaussian Processes ◽  
Extreme Values ◽  
Random Processes ◽  
Mean Square ◽  
Gaussian Random Process ◽  
Covariance Functions ◽  
Limit Formula ◽  
Image Position

In this paper the class of cyclostationary Gaussian random processes is studied. Basic asymptotics are given for the class of Gaussian processes that are centered and differentiable in mean square. Then, under certain conditions on the non-degeneration of the centered cyclostationary Gaussian process with integrable covariance functions, the Gnedenko-type limit formula is established for and all x > 0.

scholarly journals Estimation of probability of exceeding a curve by a strictly φ-sub-Gaussian quasi shot noise process

2020 ◽  
pp. 49-56
Author(s):  
O. I. Vasylyk ◽  
R. E. Yamnenko ◽  
T. O. Ianevych
Keyword(s):  
Continuous Function ◽  
Gaussian Process ◽  
Shot Noise ◽  
Gaussian Processes ◽  
Random Processes ◽  
Telecommunication Networks ◽  
Financial Mathematics ◽  
Class V ◽  
Noise Process ◽  
Shot Noise Process

In this paper, we continue to study the properties of a separable strictly φ-sub-Gaussian quasi shot noise process $X(t) = \int_{-\infty}^{+\infty} g(t,u) d\xi(u), t\in\R$, generated by the response function g and the strictly φ-sub-Gaussian process ξ = (ξ(t), t ∈ R) with uncorrelated increments, such that E(ξ(t)−ξ(s))^2 = t−s, t>s ∈ R. We consider the problem of estimating the probability of exceeding some level by such a process on the interval [a;b], a,b ∈ R. The level is given by a continuous function f = {f(t), t ∈ [a;b]}, which satisfies some given conditions. In order to solve this problem, we apply the theorems obtained for random processes from a class V (φ, ψ), which generalizes the class of φ-sub-Gaussian processes. As a result, several estimates for probability of exceeding the curve f by sample pathes of a separable strictly φ-sub-Gaussian quasi shot noise process are obtained. Such estimates can be used in the study of shot noise processes that arise in the problems of financial mathematics, telecommunication networks theory, and other applications.

scholarly journals Wavelet-based simulation of random processes from certain classes with given accuracy and reliability

2019 ◽  
Vol 25 (3) ◽  
pp. 217-225
Author(s):  
Ievgen Turchyn
Keyword(s):  
Stochastic Processes ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Random Processes

Abstract We consider stochastic processes {Y(t)} which can be represented as {Y(t)=(X(t))^{s}} , {s\in\mathbb{N}} , where {X(t)} is a stationary strictly sub-Gaussian process, and build a wavelet-based model that simulates {Y(t)} with given accuracy and reliability in {L_{p}([0,T])} . A model for simulation with given accuracy and reliability in {L_{p}([0,T])} is also built for processes {Z(t)} which can be represented as {Z(t)=X_{1}(t)X_{2}(t)} , where {X_{1}(t)} and {X_{2}(t)} are independent stationary strictly sub-Gaussian processes.

MULTIPLE MARKOV GENERALIZED GAUSSIAN PROCESSES AND THEIR DUALITIES

2010 ◽  
Vol 13 (01) ◽  
pp. 99-110 ◽  
Author(s):  
SI SI
Keyword(s):  
Stochastic Process ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Markov Property ◽  
Dual Process ◽  
Exact Form

A stochastic process describes evolutional random phenomena towards future. Corresponding with this direction, there will be a process describing, as it were, backward evolution from future to present. The dual process is a realization of this fact. We restrict our attention to Gaussian processes for which multiple Markov property is well investigated. This property expresses way of dependence of involved randomness as time goes by. We can therefore expect that such a process with multiple Markov property would present an exact form of the dual process. We shall show that having defined generalized Gaussian process with multiple Markov property, we can construct the dual process satisfying the properties that we claim. The analysis for this can be done in the space of Hida distributions.

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

Minimal distributions in a stochastic partial ordering and bounds for Gaussian processes

1983 ◽  
Vol 20 (03) ◽  
pp. 529-536
Author(s):  
W. J. R. Eplett
Keyword(s):  
Gaussian Process ◽  
Gaussian Processes ◽  
Partial Ordering ◽  
Boundary Crossing ◽  
Conditional Probabilities ◽  
Life Distribution ◽  
Life Distributions ◽  
Bounded Below ◽  
Crossing Probabilities

A natural requirement to impose upon the life distribution of a component is that after inspection at some randomly chosen time to check whether it is still functioning, its life distribution from the time of checking should be bounded below by some specified distribution which may be defined by external considerations. Furthermore, the life distribution should ideally be minimal in the partial ordering obtained from the conditional probabilities. We prove that these specifications provide an apparently new characterization of the DFRA class of life distributions with a corresponding result for IFRA distributions. These results may be transferred, using Slepian's lemma, to obtain bounds for the boundary crossing probabilities of a stationary Gaussian process.

scholarly journals Application of Stochastic Process in Signal Processing

2020 ◽  
Vol 7 (4) ◽  
pp. 71-75
Author(s):  
N John Britto
Keyword(s):  
Stochastic Process ◽  
Signal Processing ◽  
Bayesian Inference ◽  
Queuing Theory ◽  
Basic Result ◽  
Signal Strength ◽  
Internal Communication ◽  
Intermediate Node ◽  
Numerical Examples ◽  
Processing Signal

In this paper introduction about birth and death Poisson process basic result of the markovian application in queuing theory used in signal processing, signal transfer from some to passion based on the intermediate node, each intermediate node are transformed from signal strength S is directly proportional to 1/√p based on the formula using the internal communication a dependent can be characterised by the Gilbert model. Two state Markov model signals, distance when signal strength is greater the distance should be reduced. Bayesian inference is used, few numerical examples are studied.

Limit theorems for maxima and crossings of a sequence of Gaussian processes and approximation of random processes

1991 ◽  
Vol 28 (01) ◽  
pp. 17-32 ◽  
Author(s):  
O. V. Seleznjev
Keyword(s):  
Gaussian Processes ◽  
Limit Distribution ◽  
Limit Theorems ◽  
Point Processes ◽  
Random Processes ◽  
Trigonometric Polynomials ◽  
Stationary Processes ◽  
Periodic Processes

We consider the limit distribution of maxima and point processes, connected with crossings of an increasing level, for a sequence of Gaussian stationary processes. As an application we investigate the limit distribution of the error of approximation of Gaussian stationary periodic processes by random trigonometric polynomials in the uniform metric.

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