This article is cited in 38 papers

Parabolic pseudodifferential equations, hypersingular integrals, and Markov processes

A. N. Kochubei


Abstract: A fundamental solution of the Cauchy problem is constructed and investigated for the equation $\frac{\partial u}{\partial t}+Au=f$, where $A$ is a pseudodifferential operator whose symbol is a sum of homogeneous functions. The results are used for an analytic construction of discontinuous Markov processes.
Bibliography: 42 titles.

UDC: 517.43+519.21

MSC: Primary 35S10, 60J25; Secondary 42B20, 35K30

Received: 10.04.1986

 English version: Mathematics of the USSR-Izvestiya, 1989, 33:2, 233–259

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