Scatterplots to Analysis of Random Streams of Events

Khimenko, V. I.

doi:10.15217/issn1684-8853.2016.4.85

Cited by 2 publications

(1 citation statement)

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“…In the case of non-equidistant time series, we consider QMS models with stationary event flows of various types [13] or, alternatively, systems with double stochasticity [14]. Other stochastic models are also used (A. N. Shiryaev [15] et al, see, for example., [16]), in which the properties of stationary random processes are investigated.…”

Section: Introductionmentioning

confidence: 99%

Simulation of non-stationary event flow with a nested stationary component

Pleshakov

2020

Discrete and Continuous Models

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A method for constructing an ensemble of time series trajectories with a nonstationary flow of events and a non-stationary empirical distribution of the values of the observed random variable is described. We consider a special model that is similar in properties to some real processes, such as changes in the price of a financial instrument on the exchange. It is assumed that a random process is represented as an attachment of two processes - stationary and non-stationary. That is, the length of a series of elements in the sequence of the most likely event (the most likely price change in the sequence of transactions) forms a non-stationary time series, and the length of a series of other events is a stationary random process. It is considered that the flow of events is non-stationary Poisson process. A software package that solves the problem of modeling an ensemble of trajectories of an observed random variable is described. Both the values of a random variable and the time of occurrence of the event are modeled. An example of practical application of the model is given.

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Section: Introductionmentioning

confidence: 99%

Simulation of non-stationary event flow with a nested stationary component

Pleshakov

2020

Discrete and Continuous Models

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Random processes with random transitions between stable states

Khimenko

2019

Informacionno-upravlâûŝie sistemy

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Introduction: Studying random processes with several stable states and random transitions between them is important because it opens a wide range of practical problems. The detailed information structure is not studied well enough, and there is no unified approach to the description and probabilistic analysis of such processes.Purpose: Studying the main probabilistic characteristics of random processes with two stable states, and probabilistic analysis of control over chaotic transitions under various control actions.Results: We show the ways to represent and preliminarily analyze random processes with two stable states on the phase plane and in the pseudophase space. A general probabilistic model for the processes in question is proposed in the form of a two-component probabilistic «mixture» of distributions. A probabilistic analysis was carried out for the principles of control over random transitions between different states. We have defined the basic probabilistic characteristics for the processes in a management action with a variety of spectral-correlation properties and a changeable threshold for random transitions. The Poisson model of a random transition flow is analyzed with an example of «high» threshold levels.Practical relevance: The methods of visual, qualitative and analytical research in studying dynamic systems with several stable states can be combined. The proposed probabilistic models, regardless of the physical nature of the processes under consideration, can be used in problems of probabilistic analysis, control over probabilistic structure of random transitions, and simulation of physical, technical or biological systems with random switching.

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Scatterplots to Analysis of Random Streams of Events

Cited by 2 publications

References 0 publications

Simulation of non-stationary event flow with a nested stationary component

Simulation of non-stationary event flow with a nested stationary component

Random processes with random transitions between stable states

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