Summary
Seethoff and Shiflett [5] proved nice uniqueness theorems concerning doubly stochastic measures supported on the union of the graphs of two functions, but the existence theorems were more elusive. In this present paper, using a functional equations approach, not only uniqueness results but also existence theorems are obtained for doubly stochastic measures with support sets of the form g∪g-1 where g is an increasing homeomorphism of [0,1] onto itself such that g(x)<x> whenever 0<x<1.
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Sherwood, H., Taylor, M.D. Doubly stochastic measures with hairpin support. Probab. Th. Rel. Fields 78, 617–626 (1988). https://doi.org/10.1007/BF00353879
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DOI: https://doi.org/10.1007/BF00353879
Keywords
- Stochastic Process
- Probability Theory
- Functional Equation
- Statistical Theory
- Existence Theorem