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Construction of global‐in‐time solutions to Kolmogorov‐Feller pseudodifferential equations with a small parameter using characteristics |
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| Authors: | Sergio Albeverio Vladimir Danilov |
| Institution: | 1. Inst. Appl. Mathematics, SFB611, University of Bonn, Endenisher Allee 60, 53115 Bonn, Germany;2. IZKS, University of Bonn, Bruhler Str. 7, 53119 Bonn, Germany;3. BiBoS, Universities of Bielefeld and Bonn, Wegelerstrasse 6, 53115 Bonn, Germany;4. CERFIM (Locarno) Acc. Arch., Usi (Mendrisio);5. Moscow Technical University of Communications and Informatics, Aviamotornaya Str. 8a, 111020 Moscow, Russia;6. Moscow Institute of Electronics and Mathematics, B. Trehsviatitelsky per., 3?1/2, 109028 Moscow, Russia |
| Abstract: | Using an idea going back to Madelung, we construct global in time solutions to the transport equation corresponding to the asymptotic solution of the Kolmogorov‐Feller equation describing a system with diffusion, potential and jump terms. To do that we use the construction of a generalized delta‐shock solution of the continuity equation for a discontinuous velocity field. We also discuss corresponding problem of asymptotic solution construction (Maslov tunnel asymptotics). |
| Keywords: | Madelung transformation transport equation Kolmogorov‐Feller equation diffusion jump process delta‐shock solutions MSC (2010) 60G35 35Q99 41A60 |