On an Evolution Equation for a Non-Hypoelliptic Linear Partial Differential Operator from Stochastics

  • Karl Doppel

    Freie Universität Berlin, Germany
  • Niels Jacob

    University of Wales, Swansea, UK

Abstract

Recently E. B. Dynkin [2] 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 [1]. 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.

Cite this article

Karl Doppel, Niels Jacob, On an Evolution Equation for a Non-Hypoelliptic Linear Partial Differential Operator from Stochastics. Z. Anal. Anwend. 3 (1984), no. 5, pp. 425–433

DOI 10.4171/ZAA/119