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Exponential Convergence of Degenerate Hybrid Stochastic Systems with Full Dependence

In: Modern Stochastics and Applications

Author

Listed:
  • Svetlana V. Anulova

    (Russian Academy of Sciences)

  • Alexander Yu. Veretennikov

    (University of Leeds
    Russian Academy of Sciences)

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.

Suggested Citation

  • Svetlana V. Anulova & Alexander Yu. Veretennikov, 2014. "Exponential Convergence of Degenerate Hybrid Stochastic Systems with Full Dependence," Springer Optimization and Its Applications, in: Volodymyr Korolyuk & Nikolaos Limnios & Yuliya Mishura & Lyudmyla Sakhno & Georgiy Shevchenko (ed.), Modern Stochastics and Applications, edition 127, pages 159-174, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-03512-3_10
    DOI: 10.1007/978-3-319-03512-3_10
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