Skip to main content

Stochastic Differential Inclusions

  • Chapter
  • First Online:
Set-Valued Stochastic Integrals and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 157))

  • 606 Accesses

Abstract

In this chapter properties of stochastic differential inclusions are considered. The results of this chapter extend some result presented in the author monograph on the case of stochastic differential inclusions.

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 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 59.99
Price excludes VAT (USA)
  • Durable hardcover 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

References

  1. Billingsley, P.: Convergence of Probability Measures. Wiley, New York (1976)

    MATH  Google Scholar 

  2. Ikeda, N., Watanabe, S.: Stochastic Diferential Equations and Diffusion Processes. North Holland Publishing, Amsterdam (1981)

    MATH  Google Scholar 

  3. Jacod, J., Shiryaev, A.N.: Limit Theorems for Stochastic Processes. Springer, New York (1984)

    MATH  Google Scholar 

  4. Jakubowski, A., Memin, J., Pages, G.: Convergence en Loi des suites d’intégrales stochastiquies sur l’espace D 1 de Skorokhod. Probab. Theory Relat. Fields 81, 111–137 (1989)

    Article  Google Scholar 

  5. Kisielewicz, M.: Set-valued stochastic integrals and stochastic inclusions. Disc. Math. 13, 119–126 (1993)

    MathSciNet  MATH  Google Scholar 

  6. Kisielewicz, M.: Properties of solutions set of stochastic inclusions. J. Appl. Math. Stoch. Anal. 6, 217–236 (1993)

    Article  MathSciNet  Google Scholar 

  7. Kisielewicz, M.: Strong and weak solutions to stochastic inclusions. Banach Center Publ. 32, 227–286 (1995)

    Article  MathSciNet  Google Scholar 

  8. Kisielewicz, M.: Weak compactness of solution sets to stochastic differential inclusions with convex right hand sides. Topol. Math. Nonlinear Anal. 18, 149–169 (2001)

    MathSciNet  MATH  Google Scholar 

  9. Kisielewicz, M.: Backward stochastic differential inclusions. Dynam. Syst. Appl. 16, 121–140 (2007)

    MathSciNet  MATH  Google Scholar 

  10. Kisielewicz, M.: Stochastic Differential Inclusions and Applications. Springer, Berlin (2013)

    Book  Google Scholar 

  11. Kisielewicz, M.: Approximation theorems for set-valued stochastic integrals. Stoch. Anal. Appl. 36(3), 495–520 (2018)

    Article  MathSciNet  Google Scholar 

  12. Kisielewicz, M., Michta, M.: Weak solutions of set-valued stochastic differential equations. J. Math. Anal. Appl. 473, 1026–1052 (2019)

    Article  MathSciNet  Google Scholar 

  13. Michta, M.: On weak solutions to stochastic differential inclusions driven by semimartingales. Stoch. Anal. Appl. 22(5), 1341–1361 (2004)

    Article  MathSciNet  Google Scholar 

  14. Michta, M., Motyl, J.: Compactness of solutions of second order dynamical systems. Dynam. Cont. Discr. Imp. Syst. Ser. A Math. Anal. 14(4), 525–545 (2007)

    MathSciNet  MATH  Google Scholar 

  15. Motyl, J.: Stochastic functional inclusion driven by semimartingale. Stoch. Anal. Appl. 16(3), 517–532 (1998)

    Article  MathSciNet  Google Scholar 

  16. Motyl, J.: Stability problem for stochastic inclusions. Stoch. Anal. Appl. 16, 933–944 (1998)

    Article  MathSciNet  Google Scholar 

  17. Motyl, J.: Existence of solutions of set-valued equation. Bull. PAN 46(4), 419–430 (1998)

    MathSciNet  MATH  Google Scholar 

  18. Motyl, J.: Viable solutions to set-valued stochastic equations. Optimization 48, 157–176 (2000)

    Article  MathSciNet  Google Scholar 

  19. Øksendal, B.: Stochastionc Differential Equations. Springer, Berlin (1998)

    Book  Google Scholar 

  20. Stricker, C.: Loi de Semimartingales et Critères de Compacité, Sem. de Probab. XIX Lectures Notes in Mathematics, vol. 1123. Springer, Berlin (1985)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kisielewicz, M. (2020). Stochastic Differential Inclusions. In: Set-Valued Stochastic Integrals and Applications. Springer Optimization and Its Applications, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-030-40329-4_6

Download citation

Publish with us

Policies and ethics