Speaker: Vasili Kolokoltsov
Chief Research Fellow: Laboratory of Stochastic Analysis and its Applications
Abstract. About 20 years ago, extending the method of tunnel asymptotics of V.P. Maslov, the author developed the asymptotic theory (small time and/or small diffusion asymptotics) of Kolmogorov's type degenerate diffusions including multi-layered extensions, fractional diffusion (or stable) extensions and invariant processes on manifolds (e.g. stochastic geodesic flows), see monograph Semiclassical Analysis for Diffusions and Stochastic Processes, Springer Lecture Notes Math., v. 1724, Springer 2000.
After obtaining some interesting results, the author put aside investigations in this direction essentially because he had not seen sufficiently broad spectrum of possible applications.
Later, the interest of the international community to the processes of this type has been remarkably increased, due mainly to the opening of new applications in financial mathematics and new discretization results (see e.g. the paper of V. Konakov, S. Menozzi and S. Molchanov "Explicit parametrix and local limit theorems for some degenerate diffusion processes», Annales de l’ IHP, 2010, vol. 46, No.4 ).
In this talk I plan to sketch briefly the ideas of my theory aiming at looking for the perspectives of new developments in the light of new flux of research in this direction.
Research Seminar "Stochastic Analysis and its Applications in Economics"
Academic supervisors: Alexander Kolesnikov, Valentin Konakov
Language: English
Научно-исследовательский семинар "Стохастический анализ и его применения в экономике"
Преподаватели: Колесников Александр Викторович, Конаков Валентин Дмитриевич
Язык: английский