Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm

If \beta_t is renormalized self-intersection local time for planar Brownian motion, we characterize when Ee^{\gamma\beta_1} is finite or infinite in terms of the best constant of a Gagliardo-Nirenberg inequality. We prove large deviation estimates for \beta_1 and -\beta_1. We establish lim sup and lim inf laws of the iterated logarithm for \beta_t as t\to\infty.Comment: Published at http://dx.doi.org/10.1214/009117904000000504 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the asymptotics of products related to generalizations of the Wilf and Mortini problems

In this paper, we present the connection between generalized Wilf’sand Mortini’s problems. We also consider the connection betweenanother infinite product formula and limit relation with severalparameters

Inequalities and asymptotic expansions related to the volume of the unit ball in Rⁿ

Let Ωn=πn/2/Γ(n2+1)(n∈N)Ωn=πn/2/Γ(n2+1)(n∈N) denote the volume of the unit ball in RnRn. In this paper, we present asymptotic expansions and inequalities related to ΩnΩn and the quantities:Ωn−1Ωn,ΩnΩn−1+Ωn+1andΩ1/nnΩ1/(n+1)n+1

Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function

In this paper, we present some completely monotonic functions and asymptotic expansions related to the gamma function. Based on the obtained expansions, we provide new bounds for Γ(x + 1)/Γ(x + 1/2) and Γ(x + 1/2)

Firm Value, Cross-Listing Premium and the Sarbanes-Oxley Act

This paper presents empirical evidence on the effects of the Sarbanes-Oxley Act of 2002 on the value of firms and on the cross-listing choice of firms destined to three major markets in North America, Asia and Europe. We use dynamic panel data methods and treatment effects methods to find that Sarbanes-Oxley has had a negative impact on the value of firms worldwide. However, the effect of Sox on the cross-listing decision is positive in the US destination and negative in the Germany destination; and the Hong Kong destination seems to attract cross-listing of firms with lower valuations relative to the US and Germany destination. In terms of the cross-listing decision, the evidence is in favor of crowding in the market where the accounting standards are better, lending support to the signaling and bonding hypotheses of cross-listing choice.Cross-listing, Sarbanes-Oxley, dynamic panel data, treatment effects.