Generating integrable one dimensional driftless diffusions

Peter Carr, Peter Laurence, Tai Ho Wang

Research output: Contribution to journalArticlepeer-review


A criterion on the diffusion coefficient is formulated that allows the classification of driftless time and state dependent diffusions that are integrable in closed form via point transformations. In the time dependent and state dependent case, a remarkable intertwining with the inhomogeneous Burger's equation is exploited. The criterion is constructive. It allows us to devise families of driftless diffusions parametrized by a rich class of several arbitrary functions for which the solution of any initial value problem can be expressed in closed form. We also derive an elegant form for the master equation for infinitesimal symmetries, previously considered only in the time homogeneous case. To cite this article: P. Carr et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).

Original languageEnglish (US)
Pages (from-to)393-398
Number of pages6
JournalComptes Rendus Mathematique
Issue number6
StatePublished - Sep 15 2006

ASJC Scopus subject areas

  • General Mathematics


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