Семинар Добрушинской математической лаборатории ИППИ РАН
19 декабря, вторник, 16:00, ауд. 307 (очно и без трансляции).
Колокольцов Василий Никитич (ВШЭ): Fractional equations for the
scaling limits of Levy walks with position depending jump
distributions.
Abstract:
Levy walks represent important modeling tools for a variety of real
life processes. Their natural scaling limits are known to be described
by the so-called material fractional derivatives. So far these scaling
limits were derived for spatially homogeneous walks, where Fourier and
Laplace transforms represent natural tools of analysis. Here we derive
the corresponding limiting equations in the case of position depending
times and velocities of walks, where Fourier transforms cannot be
effectively applied. In fact, we derive three different limits
(specified by the way the process is stopped at an attempt to cross
the boundary), leading to three different multi-dimensional versions
of Caputo-Dzherbashian derivatives, which correspond to different
boundary conditions for the generators of the related Feller
semigroups and processes. Some other extensions and generalizations
are analyzed.
| 18.12.2023 | Комеч Сергей Александрович |