MEAN-FIELD MODELS INVOLVING CONTINUOUS-STATE-DEPENDENT RANDOM SWITCHING: NONNEGATIVITY CONSTRAINTS, MOMENT BOUNDS, and TWO-TIME-SCALE LIMITS

This work concerns mean-field models, which are formulated using stochastic differential equations. Different from the existing formulations, a random switching process is added. The switching process can be used to describe the random environment and other stochastic factors that cannot be explaine...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 15; no. 4; pp. 1783 - 1805
Main Authors Yin, G., Zhao, Guangliang, Xi, Fubao
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.08.2011
Subjects
Differential equations
Mathematical moments
Stochastic models
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ISSN1027-5487
2224-6851
2224-6851
DOI10.11650/twjm/1500406379

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Summary:This work concerns mean-field models, which are formulated using stochastic differential equations. Different from the existing formulations, a random switching process is added. The switching process can be used to describe the random environment and other stochastic factors that cannot be explained in the usual diffusion models. The added switching component makes the formulation more realistic, but it adds difficulty in analyzing the underlying processes. Several properties of the mean-field models are provided including regularity, nonnegativity, finite moments, and continuity. In addition, the paper addresses the issue when the switching takes place an order of magnitude faster than that of the continuous state. It derives a limit that is an average with respect to the invariant measure of the switching process. 2000Mathematics Subject Classification: 60J27, 60J60, 93D30. Key words and phrases: Mean-field model, Random switching, Regularity, Moment, Continuity, Ergodicity, Two-time scale.
ISSN:1027-5487
2224-6851
2224-6851
DOI:10.11650/twjm/1500406379