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Diffusion equation techniques in stochastic monotonicity and positive correlations
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  • Published: September 1991

Diffusion equation techniques in stochastic monotonicity and positive correlations

  • Ira Herbst1 &
  • Loren Pitt1 

Probability Theory and Related Fields volume 87, pages 275–312 (1991)Cite this article

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  • 36 Citations

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Summary

A diffusion equation approach is investigated for the study of stochastic monotonicity, positive correlations and the preservation of Lipschitz functions. Necessary and sufficient conditions are given for diffusion semigroups to be stochastically monotonic and to preserve the class of positively correlated measures. Applications are given which discuss the shape of the ground state for Schrödinger operators-Δ+V with FKG potentialsV.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Virginia, 22903, Charlottesville, VA, USA

    Ira Herbst & Loren Pitt

Authors
  1. Ira Herbst
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  2. Loren Pitt
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Additional information

Research supported by NSF Grant DMS 8807816.

Research supported by NSF grant DMS 8701212 and Air Force Office of Scientific Research Contract No. F49620 85C 0144.

Written while visiting, Center for Stochastic Processes, University of North Carolina.

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Herbst, I., Pitt, L. Diffusion equation techniques in stochastic monotonicity and positive correlations. Probab. Th. Rel. Fields 87, 275–312 (1991). https://doi.org/10.1007/BF01312211

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  • Issue Date: September 1991

  • DOI: https://doi.org/10.1007/BF01312211

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Keywords

  • Stochastic Process
  • Probability Theory
  • Diffusion Equation
  • Mathematical Biology
  • Lipschitz Function
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