Abstract
Pitman constructs BES3 (0) as 2M−X where X is BM1 (0) and M t =supr≤t X r . Equivalently, X−2J is BM1 (0) when X is BES3 (0) and J t =infr≥t X r . Now the fact that X−2J gives a local martingale may be extended to a general result, for linear diffusions. In particular, if X is a linear diffusion, we introduce a general class of nontrivial transformations ϕ such that Z=ϕ(X, J) is a local martingale.
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Rauscher, B. (1997). Some remarks on Pitman’s theorem. In: Azéma, J., Yor, M., Emery, M. (eds) Séminaire de Probabilités XXXI. Lecture Notes in Mathematics, vol 1655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0119312
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DOI: https://doi.org/10.1007/BFb0119312
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