Exponential Convergence of Degenerate Hybrid Stochastic Systems with Full Dependence

Svetlana V. Anulova () and Alexander Yu. Veretennikov
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Svetlana V. Anulova: Russian Academy of Sciences
Alexander Yu. Veretennikov: University of Leeds

A chapter in Modern Stochastics and Applications, 2014, pp 159-174 from Springer

Abstract: Abstract This research stems from a control problem for a suspension device. For a general class of switching stochastic mechanical systems (including closed-loop control ones), we establish the following: (1) existence and uniqueness of a weak solution and its strong Markov property, (2) mixing property in the form of the local Markov–Dobrushin condition, and (3) exponentially fast convergence to the unique stationary distribution. These results are proved for discontinuous coefficients under nondegenerate disturbances in the force field; for (3) a stability condition is additionally imposed. Linear growth of coefficients is allowed.

Keywords: Stochastic Differential Equation; Quadratic Lyapunov Function; Strong Markov Property; Switching Moment; Suspension Device (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-03512-3_10

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DOI: 10.1007/978-3-319-03512-3_10

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