ar X iv : 0 71 1 . 21 44 v 1 [ m at h . PR ] 1 4 N ov 2 00 7 Reflecting Ornstein - Uhlenbeck processes on pinned path spaces

ar X iv : 0 70 8 . 37 30 v 1 [ m at h . PR ] 2 8 A ug 2 00 7 DENSITIES FOR ROUGH DIFFERENTIAL EQUATIONS UNDER HÖRMANDER ’ S CONDITION

We consider stochastic differential equations dY = V (Y ) dX driven by a multidimensional Gaussian process X in the rough path sense. Using Malliavin Calculus we show that Yt admits a density for t ∈ (0, T ] provided (i) the vector fields V = (V1, ..., Vd) satisfy Hörmander’s condition and (ii) the Gaussian driving signal X satisfies certain conditions. Examples of driving signals include fract...

ar X iv : 0 71 1 . 23 72 v 1 [ m at h . G R ] 1 5 N ov 2 00 7 Braid groups and Artin groups

ar X iv : 0 71 1 . 05 21 v 1 [ he p - ph ] 4 N ov 2 00 7 CC DIS at α 3 s in Mellin - N and Bjorken - x spaces

Third-order results for the structure functions of charged-current deep-inelastic scattering are discussed. New results for 11’th Mellin moment for F ν p−ν̄ p 2,L structure functions and 12’th moment for F ν p−ν̄ p 3 are presented as well as corresponding higher Mellin moments of differences between the respective crossing-even and -odd coefficient functions. Approximations in Bjorken-x space for...

ar X iv : 0 71 1 . 26 95 v 1 [ m at h . SP ] 1 6 N ov 2 00 7 REGULARITY AND THE CESÀRO – NEVAI CLASS

We consider OPRL and OPUC with measures regular in the sense of Ullman–Stahl–Totik and prove consequences on the Jacobi parameters or Verblunsky coefficients. For example, regularity on [−2, 2] implies lim N →∞ N −1 [ N n=1 (a n −1) 2 +b 2 n ] = 0.

ar X iv : m at h / 04 11 35 1 v 2 [ m at h . A T ] 1 7 N ov 2 00 4 POINCARÉ SUBMERSIONS

We prove two kinds of fibering theorems for maps X → P , where X and P are Poincaré spaces. The special case of P = S yields a Poincaré duality analogue of the fibering theorem of Browder and Levine.