Boundedness vs unboundedness of Tsallis SDE: the role of overdamped approximation
- Date: Thursday 9 March 2017, 14:00 – 15:30
- Location: Mathematics Level 8, MALL 1 & 2, School of Mathematics
- Type: Statistics seminars, Seminar series
- Cost: Free
Dario Domingo, University of Leeds. Part of the probability, stochastic modelling and financial mathematics seminar series.
An apparently ideal way to generate continuous bounded stochastic processes is to consider the stochastically perturbed motion of a point of small mass in an infinite potential well, under overdamped approximation. Here, we show that the above procedure can be fallacious by providing a counter-example concerning one of the most employed bounded noises (Tsallis noise), which admits the Tsallis q-statistics as stationary density. We show that for negative values of q (corresponding to sufficiently large diffusion coefficient of the stochastic force), the motion resulting from the overdamped approximation is unbounded. We then investigate the cause of the failure of Kramers' first type approximation, and we formally show that the solutions of the full Newtonian non-approximated model are bounded, following the physical intuition.
Finally, we provide a new family of noises extending the TSB noise, always bounded independently of the value of q.
This is joint work with Alberto d'Onofrio and Franco Flandoli.
Dario Domingo, University of Leeds