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.
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Anulova, S.V., Veretennikov, A.Y. (2014). Exponential Convergence of Degenerate Hybrid Stochastic Systems with Full Dependence. In: Korolyuk, V., Limnios, N., Mishura, Y., Sakhno, L., Shevchenko, G. (eds) Modern Stochastics and Applications. Springer Optimization and Its Applications, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-03512-3_10
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