Skip to main content

Averaging for martingale problems and stochastic approximation

  • Conference paper
  • First Online:
Book cover Applied Stochastic Analysis

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 177))

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bensoussan, A., Lions, J. L., and Papanicolaou, G. C. (1978). Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam.

    Google Scholar 

  • Bhattacharya, R. N., Gupta, V. K., and Walker, H. F. (1989). Asymptotics of solute dispersion in periodic porous media. SIAM J. Appl. Math. 49, 86–98.

    Article  Google Scholar 

  • Dupuis, Paul and Kushner, Harold J. (1989). Stochastic approximation and large deviations: upper bounds and w.p. 1 convergence. SIAM J. Control Optim., 27, 1108–1135.

    Article  Google Scholar 

  • Ethier, Stewart N. and Kurtz, Thomas G. (1986). Markov Processes: Characterization and Convergence. Wiley, New York.

    Google Scholar 

  • Griego, Richard J. and Hersh, Reuben (1969). Random evolutions, Markov chains, and systems of partial differential equations. Proc. Nat. Acad. Sci. USA 62, 305–308.

    Google Scholar 

  • Hersh, Reuben (1974). Random evolutions: a survey of results and problems. Rocky Mt. J. Math. 4, 443–477.

    Google Scholar 

  • Kallenberg, Olav (1986). Random Measures. Academic Press, New York.

    Google Scholar 

  • Khas'minskii, R. Z. (1966a). On stochastic processes defined by differential equations with a small parameter. Theory Probab. Appl. 11, 211–228.

    Article  Google Scholar 

  • Khas'minskii, R. Z. (1966b). A limit theorem for the solutions of differential equations with random right-hand sides. Theory Probab. Appl. 11, 390–406.

    Article  Google Scholar 

  • Kurtz, Thomas G. (1972). Inequalities for the law of large numbers. Ann. Math. Statist. 43, 1874–1883.

    Google Scholar 

  • Kurtz, Thomas G. (1973). A limit theorem for perturbed operator semigroups with applications to random evolutions. J. Funct. Anal. 12, 55–67.

    Article  Google Scholar 

  • Kurtz, Thomas G. (1987). Martingale problems for controlled processes. Stochastic Modeling and Filtering. Lecture Notes in Control and Information Sci. 91, Springer-Verlag, Berlin.

    Google Scholar 

  • Kushner, Harold J. (1979). Jump-diffusion approximation for ordinary differential equations with wide-band random right hand sides. SIAM J. Control Optim. 17, 729–744.

    Article  Google Scholar 

  • Kushner, Harold J. (1984). Approximation and Weak Convergence Methods for Random Processes with Applications to Stochastic Systems Theory. MIT Press, Cambridge, Mass.

    Google Scholar 

  • Kushner, Harold J. and Clark, Dean S. (1978). Stochastic Approximation Methods for Constrained and Unconstrained Systems. Springer-Verlag, Berlin.

    Google Scholar 

  • Kushner, Harold J. and Schwartz, Adam (1984). An invariant measure approach to the convergence of stochastic approximations with state dependent noise. SIAM J. Control Optim., 22, 13–27.

    Article  Google Scholar 

  • Lochak, P. and Meunier, C. (1988). Multiphase Averaging for Classical Systems. Springer-Verlag, New York.

    Google Scholar 

  • Metivier, Michel and Priouret, Pierre (1984). Applications of a Kushner and Clark lemma to general classes of stochastic algorithms. IEEE Trans. Information Theory 30, 140–151.

    Article  Google Scholar 

  • Papanicolaou, G. C. (1978). Asymptotic analysis of stochastic equations. Studies in Probability Theory, MAA Studies 18, M. Rosenblatt, ed. Mathematics Association of America, New York, 111–179.

    Google Scholar 

  • Pinsky, Mark A. (1974). Multiplicative operator functionals and their asymptotic properties. Advances in Probability 3, Dekker, New York.

    Google Scholar 

  • Stockbridge, Richard H. (1990). Time-average control of martingale problems: Existence of a stationary solution. Ann. Probab. 18, 190–205.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Ioannis Karatzas Daniel Ocone

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag

About this paper

Cite this paper

Kurtz, T.G. (1992). Averaging for martingale problems and stochastic approximation. In: Karatzas, I., Ocone, D. (eds) Applied Stochastic Analysis. Lecture Notes in Control and Information Sciences, vol 177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007058

Download citation

  • DOI: https://doi.org/10.1007/BFb0007058

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55296-3

  • Online ISBN: 978-3-540-47017-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics