Stochastic models of piecewise-constant and piecewise-linear non-Gaussian processes based on Poisson flows

Огородников, В. А.; Sereseva, Olga V.; Kargapolova, Nina

doi:10.1515/rnam-2016-0018

Cited by 3 publications

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“…The issues related to the study of different types of piecewise-linear processes on point flows were considered in [3][4][5][6][7][8]. Those processes are modifications of piecewise-constant processes on point flows proposed and studied previously in [2].…”

Section: Msc 2010: 60g55 65c05mentioning

confidence: 99%

“…In this paper we study an approach to calculation of the correlation function and characteristics of the random process related to it [4]:…”

Section: Statistical Characteristics Of a Piecewise-linear Process Onmentioning

confidence: 99%

“…Based on estimates of the correlation function r(t, t + h) of process (1.1) obtained from model samples for the case F(x) = 1 − exp(−λx), λ = 0.25 with different values of t, it was shown in [4] that for t > 7.5 the process becomes close to a stationary one in its correlations, a similar behaviour of the process is observed relative to means and variances. Examples of correlation functions r(t, τ) of the process Y(t) for t = 20 were also presented in that paper for different values of the parameter λ.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The typical peculiarity of such processes is that the segments of a piecewise-linear function form a discontinuous function. These researches have shown a prospect of using simulation algorithms for piecewise-linear processes to solve practical problems.The issues related to the study of different types of piecewise-linear processes on point flows were considered in [3][4][5][6][7][8]. Those processes are modifications of piecewise-constant processes on point flows proposed and studied previously in [2].…”

mentioning

confidence: 99%

“…The way of specification of random values in Poisson processes essentially determines the properties of the process. Thus, for example, specifying additive random variables [3] with successively increasing number of summands at flow points, we get a non-stationary process, and specifying them as independent identically distributed random variables [4,5], we get an asymptotically stationary one. In particular, one-point characteristics were considered for such types of processes and their asymptotic properties were studied.…”

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confidence: 99%

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Probabilistic properties of non-Gaussian piecewise-linear processes on Poisson flows with independent random values at points of flow

Огородников

Sereseva

2018

Russian Journal of Numerical Analysis and Mathematical Modelling

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Abstract:The paper is focused on study of non-stationary piecewise-linear processes on Poisson point flows with independent identically distributed random variables at support points. An approach to calculate the correlation function of the process on the base of the total probability formula is considered. A general expression for the correlation function of a non-stationary process is obtained. Particular cases are considered. Using the method of direct simulation, it is shown numerically that the correlation function of the process has a point of inflection.Keywords: Random process, Poisson flow, correlation function. MSC 2010: 60G55, 65C05Some approaches to modelling the piecewise-linear non-Gaussian processes on point flows were considered in [1] relative to simulation of price series and the study of various trading algorithms based on these models. The corresponding models use intervals between points of flow and the distributions of process values at support points as input characteristics. Various approaches to construction of processes were considered, in particular, the alternation of distributions for ascending and descending sections of the polyline was used with the help of a special Markov chain.Special piecewise-linear processes were used in [9] for construction of models for climate prediction. The typical peculiarity of such processes is that the segments of a piecewise-linear function form a discontinuous function. These researches have shown a prospect of using simulation algorithms for piecewise-linear processes to solve practical problems.The issues related to the study of different types of piecewise-linear processes on point flows were considered in [3][4][5][6][7][8]. Those processes are modifications of piecewise-constant processes on point flows proposed and studied previously in [2]. One has to specify probabilistic characteristics of point flows and distribution of random variables at those points to apply numerical stochastic modelling of piecewise-linear processes which, in their turn, may be used for description of some real processes, for example, for modelling solar radiation scattering processes in stochastic cloudy media, modelling climate series, etc. The way of specification of random values in Poisson processes essentially determines the properties of the process. Thus, for example, specifying additive random variables [3] with successively increasing number of summands at flow points, we get a non-stationary process, and specifying them as independent identically distributed random variables [4,5], we get an asymptotically stationary one. In particular, one-point characteristics were considered for such types of processes and their asymptotic properties were studied. An approach to the study of correlation structure of piecewise-linear processes on Poisson flows was proposed in [5].In this paper we present the results of study of a process on Poisson flows whose values are IIDRV with finite variance at Poisson support points. Considering processes of such type, we obtained...

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Section: Msc 2010: 60g55 65c05mentioning

confidence: 99%

“…In this paper we study an approach to calculation of the correlation function and characteristics of the random process related to it [4]:…”

Section: Statistical Characteristics Of a Piecewise-linear Process Onmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Probabilistic properties of non-Gaussian piecewise-linear processes on Poisson flows with independent random values at points of flow

Огородников

Sereseva

2018

Russian Journal of Numerical Analysis and Mathematical Modelling

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Signal Modeling with IG Noise and Parameter Estimation Based on RJMCMC

Fauzy¹,

Suparman²,

Supandi³

2022

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Piecewise constant (PC) is a stochastic model that can be applied in various fields such as engineering and ecology. The stochastic model contains a noise. The accuracy of the stochastic model in modeling a signal is influenced by the type of noise. This paper aims to propose inverse-gamma noise in the PC model and the procedure for estimating the model parameters. The model parameters are estimated using the Bayes approach. Model parameters have a variable dimension space so that the Bayesian estimator cannot be determined analytically. Therefore, the Bayesian estimator is calculated using the reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm. The performance of the RJMCMC algorithm is validated using data synthesis. The finding is a new PC model in which the noise has an inverse-gamma distribution. In addition, this paper also proposes a parameter estimation procedure for the model based on an RJMCMC. The simulation study shows that the model parameter estimators generated by this algorithm are close to the model parameter values. This paper concludes that inverse gamma noise can be used as an alternative noise in the PC model. The RJMCMC is categorized as a valid algorithm and can estimate the PC model parameters where the noise has an inverse-gamma distribution. The novelty in this paper is the development of a new stochastic model and the procedure for estimating the model parameters. In application, the findings in this paper have the potential to improve the suitability of the stochastic model to the signal.

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Medical Image Segmentation and Analysis

Kashyap

2019

Advances in Medical Technologies and Clinical Practice

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An improved energy-based technique with a Lattice Boltzmann method organizes with the neighborhood and global energy terms, local term propels to pull the frame and constrain it to protest limit, decides noteworthy points of interest not confined to, snappy planning, automation, invariance of exact medical image segmentation, and analysis. Consequently, the worldwide vitality fitting term drives the advancement of the frame at a division of the question limit. The worldwide vitality term relies upon the worldwide division computation, which can better catch drive information of pictures than mixture area-based dynamic shape technique. Both neighborhood and worldwide terms are ordinarily acclimatized to construct a level set strategy to divide pictures with exactness. The level set technique with Boltzmann system uses neighborhood mean, a quality which engages it as far as possible. The proposed chapter gathers gainful purposes of intrigue not stuck just using expedient process, computerization, and right helpful picture partitions.

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Stochastic models of piecewise-constant and piecewise-linear non-Gaussian processes based on Poisson flows

Cited by 3 publications

References 0 publications

Probabilistic properties of non-Gaussian piecewise-linear processes on Poisson flows with independent random values at points of flow

Probabilistic properties of non-Gaussian piecewise-linear processes on Poisson flows with independent random values at points of flow

Signal Modeling with IG Noise and Parameter Estimation Based on RJMCMC

Medical Image Segmentation and Analysis

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