On reflected diffusions in cones and cylinders

Oleksii  Kulyk; Andrey Pilipenko; Sylvie Rœlly

doi:10.3842/umzh.v75i11.7418

Oleksii Kulyk Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Poland
Andrey Pilipenko Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv and National Technical University of Ukraine ,,Igor Sikorsky Kyiv Polytechnic Institute''
Sylvie Rœlly Institut für Mathematik, Universität Potsdam, Germany

DOI: https://doi.org/10.3842/umzh.v75i11.7418

Анотація

УДК 519.21

Про відбиті дифузії в конусах і циліндрах

Нехай $X$ – дифузія в конусі зі скісним відбиттям на межі. Вивчається питання про можливість досягнення дифузією $X$ вершини конуса за скінченний час з додатною ймовірністю. Запропоновано новий імовірнісний метод дослідження, що пов'язаний з довготривалою поведінкою дифузії, відбитої в циліндрі.

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