Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1984-10-31
On an Evolution Equation for a Non-Hypoelliptic Linear Partial Differential Operator from StochasticsKarl Doppel and Niels Jacob (1) Freie Universität Berlin, Germany
(2) University of Wales, Swansea, UK
Recently E. B. Dynkin  introduced and studied a non-hypoelliptic linear partial differential operator of even order (with constant coefficients) which originates from the theory of multi-parametric stochastic processes. Motivated by the consideiations of Dynkin the authors have solved a generalized Dirichlet problem for this differential operator in their work . Our aim in the present paper is to investigate the Cauchy problem for the corresponding evolution equation (in the time variable of first order); such a Cauchy problem could have applications to some questions from the stochastics.
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Doppel Karl, Jacob Niels: On an Evolution Equation for a Non-Hypoelliptic Linear Partial Differential Operator from Stochastics. Z. Anal. Anwend. 3 (1984), 425-433. doi: 10.4171/ZAA/119