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In this note we study simple modules for a reduced enveloping algebra Ux (g) in the critical case when X E 2 g^x is “nilpotent”. Some dimension formulas computed by Jantzen suggest modified versions o...
Originally devised for baseball, the Pythagorean Won-Loss formula estimates the percentage of games a team should have won at a particular point in a season. For decades, this formula had no mathemat...
In the paper a stochastic generalization of the Taylor formula for It6 processes of diffusion type is investigated with respect to mean square, almost sure and weak convergence.
A functional calculus based on Feynman-Kac formula
The purpose of the present paper is to prove a stochastic Taylor formula for two-parameter processes which extends the results of W. Wagner and E. Platen in the one-parameter case (6. C51-C71).
We calculate Voicdescu's R-transform of the compactly supported probability measure on R induced from the orthogonal polynomials with a constant recursion formula, and investigate its infinite divi...
For the second derivative, an analogue of the classical Taylor's formula i s considered on a suitable function space. The sum of the "Taylor series" represents the Gauss semigroup. This may be usefu...
In this paper,we use the Malliavin calculus techniques to obtain an anticipative version of the change of variable formula forLevy processes.Here th coefficients are in the domain of the anihilation...
A Percolation Formula     SLE  Cardy  conformal invariance       2009/5/4
Let A be an arc on the boundary of the unit disk U. We prove an asymptotic formula for the probability that there is a percolation cluster K for critical site percolation on the triangular grid in U w...
A different but very short proof of a recent result of Khoshnevisan.
It was proved by Michel Talagrand in [10] that the Parisi formula for the free energy in the Sherrington-Kirkpatrick model is differentiable with respect to inverse temperature parameter. We present a...
Let H be a separable real Hilbert space and let F = (Ft)t in [0,T] be the augmented filtration generated by an H-cylindrical Brownian motion WH on [0,T] on a probability space (Ω,F,P). We prove that i...
We use Haff’s fundamental identity to express the expectation of Sp in lower-order terms, where Sfollows the central Wishart distribution.

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