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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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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DOI: https://doi.org/10.1007/BF01312211
Keywords
- Stochastic Process
- Probability Theory
- Diffusion Equation
- Mathematical Biology
- Lipschitz Function