Limit behavior of two-time-scale diffusions revisited

Large Space-Time Scale Behavior of Linearly Interacting Diffusions

We study a renormalization transformation arising in an infinite system of interacting diffusions. The components of the system are labeled by the N -dimensional hierarchical lattice (N ≥ 2) and take values in a compact convex set D ⊂ Rd (d ≥ 1). Each component starts at some θ ∈ D and is subject to two motions: (1) an isotropic diffusion according to a local diffusion rate g : D → [0,∞) chosen...

Large Deviations for Two-Time-Scale Diffusions, With Delays

We consider the problem of large deviations for a two-time-scale reflected diffusion process, possibly with delays in the dynamical terms. The Dupuis-Ellis weak convergence approach is used. It is perhaps the most intuitive and simplest for the problems of concern. The results have applications to the problem of approximating optimal controls for twotime-scale systems via use of the averaged eq...

Large Scale Behavior of a System of Interacting Diffusions

We present the explicit derivation of the asymptotic law of the tagged particle process for a system of interacting Brownian motions in the presence of a diffusive scaling in non-equilibrium. The interaction is local and interpolates between the totally independent case (non-interacting) and the totally reflecting case. It can be viewed as the limiting local version of an interaction through a ...

On oscillatory behavior of two-dimensional time scale systems

where a,b ∈ Crd([t0,∞)T,R+), and f and g are nondecreasing functions such that uf (u) > 0 and ug(u) > 0 for u = 0. The time scale theory is initiated by the German mathematician S. Hilger in his PhD thesis in 1988. His purpose was to unify continuous and discrete analysis and extend the results in one theory. A time scale, denoted by T, is a nonempty closed subset of real numbers, and some exam...

Class of Limit Theorems for Singular Diffusions