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Lipschitz continuous processes for given marginals

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  • Dubischar, Daniel

Abstract

For two Borel probability measures P and Q on a complete separable metric space X the minimal L[infinity]-distance is defined as l[infinity](P,Q):=inf{[var epsilon]>0: P(A)[less-than-or-equals, slant]Q(A[var epsilon]) [for all]A[subset of]X}. We show that for every l[infinity]-Lipschitz continuous collection of measures there exists a Lipschitz continuous process with one-dimensional distributions Pt. This correspondence fails in higher dimensional parameter sets.

Suggested Citation

  • Dubischar, Daniel, 2003. "Lipschitz continuous processes for given marginals," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 45-48, March.
    • Handle: RePEc:eee:stapro:v:62:y:2003:i:1:p:45-48
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