Exponential ergodicity for SDEs and McKean-Vlasov processes with L\'{e}vy noise

We study stochastic differential equations (SDEs) of McKean-Vlasov type with distribution dependent drifts and driven by pure jump L\'{e}vy processes. We prove a uniform in time propagation of chaos result, providing quantitative bounds on convergence rate of interacting particle systems with L\'{e}vy noise to the corresponding McKean-Vlasov SDE. By applying techniques that combine couplings, appropriately constructed $L^1$-Wasserstein distances and Lyapunov functions, we show exponential convergence of solutions of such SDEs to their stationary distributions. Our methods allow us to obtain results that are novel even for a broad class of L\'{e}vy-driven SDEs with distribution independent coefficients.Comment: 36 page

Exploring Be phenomena in OBA stars: a Mid-infrared search

As early-type stars with a rotation speed close to their critical velocity, Be stars experience an event called the Be phenomenon. The material in their equator is ejected into outside space during the Be phenomenon and forms a circumstellar disk. The mechanism triggering these events remains poorly understood, and observations of these events are limited because the duration of these events ranges from months to years. Long-term epoch photometry in the infrared bands is expected to be ideal for detecting Be phenomena because the brightness variation is larger, and the effect of interstellar extinction is weaker as well. We conducted a systematic search for Be phenomena among Milky Way OBA stars in the mid-infrared. We examined the brightness and colour variations of known classical Be stars using the WISE W1 and W2 photometry bands to quantify their characteristics. Subsequently, we established a set of criteria to identify similar photometric variations in a large sample of OBA stars. We found 916 OBA stars that show Be phenomena in the past 13 years, 736 of which are newly discovered. The peak-to-peak variations in magnitude and colour were found to be correlated, indicating that a decretion disk is common. The increase in colour was observed to be strongly correlated with the emission of the H-alpha line, providing further evidence of the association with circumstellar disks. The brightness variation of a star with Be phenomena can be up to 1.5 mag, and the colour variations can be up to 0.4 mag. The median durations for the disk build-up and decay phases are 474 and 524 days, respectively (durations shorter than 180 days are not sampled). The search for Be phenomena in the WISE bands greatly enlarges the number of stars showing disk variation, and it enables multi-band photometry analysis of these events with the help of current and future optical photometry surveys.Comment: 14 pages, 16 figures, 5 tables, accepted for publication in A&