Mean stochastic comparison of diffusions

  • Bruce Hajek

DOI: 10.1007/BF00532643

Cite this article as:
Hajek, B. Z. Wahrscheinlichkeitstheorie verw Gebiete (1985) 68: 315. doi:10.1007/BF00532643


Stochastic bounds are derived for one dimensional diffusions (and somewhat more general random processes) by dominating one process pathwise by a convex combination of other processes. The method permits comparison of diffusions with different diffusion coefficients. One interpretation of the bounds is that an optimal control is identified for certain diffusions with controlled drift and diffusion coefficients, when the reward function is convex. An example is given to show how the bounds and the Liapunov function technique can be applied to yield bounds for multidimensional diffusions.


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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Bruce Hajek
    • 1
  1. 1.Department of Electrical and Computer Engineering and the Coordinated Science LaboratoryUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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