Skip to main content

Almost sure instability of a class of linear stochastic systems with jump process coefficients

  • Part II: Linear Stochastic Systems. Stability Theory
  • Conference paper
  • First Online:
Lyapunov Exponents

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1186))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.Z. Khas'minskii, “Necessary and sufficient conditions for the asymptotic stability of linear stochastic systems,” Theory Prob. Appl. vol. 12, pp. 144–147 (1967).

    Article  MathSciNet  Google Scholar 

  2. R.Z. Khas'minskii, Stochastic Stability of Differential Equations, Sijthoff and Noordhoof, Alphan aan den Rijn, The Netherlands (1980).

    Chapter  Google Scholar 

  3. M. Pinsky, “Stochastic stability and the Dirichlet problem,” Comm. Pure Appl. Math. vol. 27, pp. 311–350 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  4. F. Kozin and S. Prodromou, “Necessary and sufficient conditions for almost sure sample stability of linear Ito equations,” SIAM J. Appl. Math. vol. 21, pp. 413–424 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  5. R.R. Mitchell and F. Kozin, “Sample stability of second order linear differential equations with wide band noise coefficients,” SIAM J. Appl. Math. vol. 27, pp. 571–605 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  6. G.L. Blankenship and G.C. Papanicolaou, “Stability and control of stochastic systems with wide-band noise disturbances I,” SIAM J. Appl. Math. vol. 34, pp. 437–476 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  7. C.W. Li, “Almost Sure Stability, Optimal Control and Scheduling of Stochastic Systems with Point Process Coefficients,” Ph.D. Dissertation, Applied Mathematics Program, University of Maryland, College Park (June 1984).

    Google Scholar 

  8. G.L. Blankenship, “Stability of stochastic differential equations with random coefficients,” IEEE Trans. Automatic Control vol. AC-22, pp. 834–838 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  9. M.M. Benderskii and L. Pastur, “On the spectrum of the one-dimensional Schrodinger equation with a random potential,” Math. USSR Sbornik vol. 11, pp. 245–256 (1970).

    Article  MathSciNet  Google Scholar 

  10. M.M. Benderskii and L. Pastur, “Calculation of the average number of states in a model problem,” Soviet Physics JETP vol. 30, pp. 158–162 (1970).

    Google Scholar 

  11. L. Pastur and E.P. Fel'dman, “Wave transmittance for a thick layer of a randomly inhomogeneous medium,” Soviet Physics JETP vol. 40, pp. 241–243 (1975).

    Google Scholar 

  12. K.A. Loparo, “Stability of Nonlinear and Stochastic Systems,” Ph.D. Dissertation, Systems Engineering Department, Case Western Reserve University, Cleveland (1977).

    Google Scholar 

  13. G.C. Papanicolaou, “Wave propagation and heat conduction in a random medium,” pp. 193–218 in Stochastic Differential Equations, ed. J.P. Cecconi, CIME Liguori Editore, Napoli (1978).

    Google Scholar 

  14. S. Kotani, “On a growth of solutions of second order linear differential equations with random coefficients,” pp. 153–161 in Proc. International Symp. Stochastic Differential Equations, ed. K. Ito,, Kyoto (1976).

    Google Scholar 

  15. S. Kotani, “On asymptotic behavior of the spectra of a one-dimensional Hamilitonian with certain random coefficient,” Publ. RIMS Kyoto University vol. 12, pp. 447–492 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  16. D.H. Hodges and R.O. Ormiston, “Stability of elastic bending and torsion of uniform cantilever rotor blades in hover with variable structural coupling,” NASA Tech. Note (April 1976).

    Google Scholar 

  17. G.L. Blankenship and W.E. Hopkins, Jr., “Wind turbine rotor blade stability in turbulent flows,” Proc. DOE/OER Symp. on Nonlinear Problems in Energy Systems, Argonne National Laboratory (April 1983).

    Google Scholar 

  18. K. Ito and H.P. McKean, Diffusion Processes and Their Sample Paths, Springer-Verlag, Berlin (1965).

    Book  MATH  Google Scholar 

  19. G.L. Blankenship, W.E. Hopkins, Jr., and N. Barkakati, “Stochastic Dynamical Models of Wind Turbine Generation Systems,” Final report DOE/OER Contract DE-AC05-81-ER10869 (October 1984).

    Google Scholar 

Download references

Authors

Editor information

Ludwig Arnold Volker Wihstutz

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Loparo, K.A., Blankenship, G.L. (1986). Almost sure instability of a class of linear stochastic systems with jump process coefficients. In: Arnold, L., Wihstutz, V. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076838

Download citation

  • DOI: https://doi.org/10.1007/BFb0076838

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16458-6

  • Online ISBN: 978-3-540-39795-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics