Open AccessSpace-time Poisson Flow Intensity Density with Zero Occurrence Probability on Stochastic Subsets of Its Spatial Definition Domain
Author(s) -
В. В. Хуторцев
Publication year - 2020
Publication title -
matematika i matematičeskoe modelirovanie
Language(s) - English
Resource type - Journals
ISSN - 2412-5911
DOI - 10.24108/mathm.0320.0000214
Subject(s) - poisson distribution , flow (mathematics) , mathematics , intensity (physics) , probability density function , mathematical analysis , space time , space (punctuation) , domain (mathematical analysis) , stochastic process , statistical physics , geometry , statistics , physics , computer science , quantum mechanics , chemical engineering , engineering , operating system
Object of research: space-time Poisson flows. Subject of research: influence patterns of the stochastic subset characteristics of the spatial definition domain of the space-time Poisson flow on its intensity density. Work objective: to determine a relationship between the space-time Poisson flow intensity density and the characteristics of the inhomogeneity subdomains of the spatial definition domain where this flow is specified. A problem to be solved: to determine the space-time Poisson flow intensity density to meet a selected criterion, i.e. a conditional intensity density, where the condition is that the points in the flow state space belong to the stochastic inhomogeneity subdomains. We consider a space-time Poisson flow whose spatial domain contains stochastic subdomains of inhomogeneity. An equality criterion to zero occurrence probability generated by this flow in the inhomogeneity subdomains is used to derive an expression for the flow intensity density. The case has been considered when positions of inhomogeneity subdomain centers are random, and their angular positions relative to these centers and their shapes are defined and unchanged at analysis interval. To describe them, we used the probability densities of the inhomogeneity subdomain centers, which are time variant. A theorem is proved that substantiates the structure of the intensity density of the space-time Poisson flow with a stochastic inhomogeneous spatial domain of definition. The relationship of this characteristic with the probabilistic characteristics of inhomogeneity subdomain parameters is shown. Examples are given to illustrate a procedure for determining the intensity densities of space-time Poisson flows for both stochastic and deterministic structures of inhomogeneity subdomains. It is shown that for the stochastic case, taking into account the random nature of their location leads to a solution significantly different from the singular case. The scope of possible practical use of the results obtained for tasks related to the search for objects of observation is determined.