The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-field Stochastic Differential Equations

In this paper, some properties of a stochastic convolution driven by tempered fractional Brownian motion are obtained. Based on this result, we get the existence and uniqueness of stochastic mean-field equation driven by tempered fractional Brownian motion. Furthermore, combining with the Banach fixed point theorem and the properties of Mittag-Leffler functions, we study the existence and uniqueness of mild solution for a kind of time fractional mean-field stochastic differential equation driven by tempered fractional Brownian motion.     

Compound Poisson approximation for unbounded functions on a group,with application to large deviations

Summary A second order error bound is obtained for approximating h d by h d , where is a convolution of measures andQ a compound Poisson measure on a measurable abelian group, and the functionh is not necessarily bounded. This error bound is more refined than the usual total variation bound in the sense that it contains the functionh. The method used is inspired by Stein's method and hinges on bounding Radon-Nikodym derivatives related to . The approximation theorem is then applied to obtain a large deviation result on groups, which in turn is applied to multivariate Poisson approximation.Research of the second author was supported by Schweizerischer Nationalfonds     

Differential operator Lie algebras on the ring of Laurent polynomials

A class of differential operator Lie algebras on the unit circle is introduced and discussed. They are the natural generalizations of the Witt algebra and the Virasoro algebra. Among them are the higher-spin algebrasW ₁₊ andW which occur in the physics literature.     

Analogues of hadwiger's theorem in space ℝ n —Sufficient conditions for a convex domain to enclose another

We estimate the kinematic measure of one convex domain moving to another under the groupG of rigid motions in ⁿ . We first estimate the kinematic formula for the total scalar curvature D ₀gD ₁ Rdv of then–2 dimensional intersection submanifold D ₀gD ₁. Then we use Chern and Yen's kinematic fundamental formula and our integral inequality to obtain a sufficient condition for one convex domain to contain another in ⁿ (4). Forn=4, we directly obtain another sufficient condition in ⁴.