Skip to main content
Log in

Stochastic Equations and Inclusions with Mean Derivatives and Some Applications

Optimal Solutions for Inclusions of Geometric Brownian Motion Type

  • Published:
Methodology and Computing in Applied Probability Aims and scope Submit manuscript

Abstract

The paper is devoted to a brief introduction into the theory of equations and inclusions with mean derivatives and to investigation of a special type of such inclusions called inclusions of geometric Brownian motion type. The existence of optimal solutions maximizing some cost criteria, is proved.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aubin J-P, Cellina A (1984) Differential inclusions. Set-valued maps and viability theory. Springer, Berlin

    Book  MATH  Google Scholar 

  • Azarina SV, Gliklikh YE (2007) Differential inclusions with mean derivatives. Dyn Syst Appl 16:49–72

    MATH  MathSciNet  Google Scholar 

  • Azarina SV, Gliklikh YE (2009) Inclusions with mean derivatives for porcesses of geometric Brownian motion type and their applications. In: Seminar on global and stochastic analysis, vol 4 (in Russian), pp 3–8

  • Billingsley P (1969) Convergence of probability measures. Wiley, New York

    Google Scholar 

  • Borisovich YG, Gelman BD, Myshkis AD, Obukhovskii VV (2005) Introduction to the theory of multi-valued mappings and differential inclusions. KomKniga, Moscow (in Russian)

    Google Scholar 

  • Conway ED (1971) Stochastic equations with discontinuous drift. Trans Am Math Soc 157(1):235–245

    Article  MATH  MathSciNet  Google Scholar 

  • Gihman II, Skorohod AV (1979) Theory of stochastic processes, vol 3. Springer, New York

    Book  Google Scholar 

  • Gliklikh YE (2011) Global and stochastic analysis with applications to mathematical physics. Springer, London

    Book  MATH  Google Scholar 

  • Gliklikh YE, Obukhovskiĭ AV (2001) Stochastic differential inclusions of Langevin type on Riemannian manifolds. Discuss. Math. DICO 21:173–190

    MATH  Google Scholar 

  • Kantorovich LV, Akilov GP (1982) Functional analysis. Pergamon Press, Oxford

    MATH  Google Scholar 

  • Kisielewicz M (1997) Stochastic differential inclusions. Discuss. Math. DICO 17(1–2):51–65

    MATH  MathSciNet  Google Scholar 

  • Kree P (1982) Diffusion equation for multivalued stochastic differential equation. J Func Anal 49:73–90

    Article  MATH  MathSciNet  Google Scholar 

  • Motyl J (1995) On the solution of stochastic differential inclusion. J Math Anal Appl 192:117–132

    Article  MATH  MathSciNet  Google Scholar 

  • Nelson E (1966) Derivation of the Schrödinger equation from Newtonian mechanics. Phys Rev 150:1079–1085

    Article  Google Scholar 

  • Nelson E (1967) Dynamical theory of Brownian motion. Princeton University Press, Princeton

    Google Scholar 

  • Nelson E (1985) Quantum fluctuations. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Parthasarathy KR (1978) Introduction to probability and measure. Springer, New York

    Google Scholar 

  • Yosida Y (1965) Functional analysis. Springer, Berlin

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yuri E. Gliklikh.

Additional information

The research is supported in part by RFBR Grant 12-01-00183.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gliklikh, Y.E., Zheltikova, O.O. Stochastic Equations and Inclusions with Mean Derivatives and Some Applications. Methodol Comput Appl Probab 17, 91–105 (2015). https://doi.org/10.1007/s11009-013-9373-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11009-013-9373-4

Keywords

AMS 2000 Subject Classifications

Navigation