Analytic proof of multivariate stable local large deviations and application to deterministic dynamical systems
Ian Melbourne, Dalia Terhesiu
Abstract
We give a short analytic proof of local large deviations for i.i.d. random variables in the domain of a multivariate α-stable law, α∈(0,1)∪(1,2]. Our method simultaneously covers lattice and nonlattice distributions (and mixtures thereof), bypassing aperiodicity considerations. The proof applies also to the dynamical setting.
Topics & Concepts
MathematicsMultivariate statisticsLarge deviations theoryDynamical systems theoryLattice (music)Statistical physicsDomain (mathematical analysis)Random variableApplied mathematicsPure mathematicsMathematical analysisStatisticsPhysicsQuantum mechanicsAcousticsMathematical Dynamics and FractalsStochastic processes and statistical mechanicsFunctional Equations Stability Results