The algebra of bounded holomorphic martingales
نویسندگان
چکیده
منابع مشابه
SLE martingales and the Virasoro algebra
We present an explicit relation between representations of the Virasoro algebra and polynomial martingales in stochastic Loewner evolutions (SLE). We show that the Virasoro algebra is the spectrum generating algebra of SLE martingales. This is based on a new representation of the Virasoro algebra, inspired by the Borel-Weil construction, acting on functions depending on coordinates parametrizin...
متن کاملBounded Holomorphic Functions on Bounded Symmetric Domains
Let D be a bounded homogeneous domain in C , and let A denote the open unit disk. If z e D and /: D —► A is holomorphic, then ß/(z) is defined as the maximum ratio \Vz(f)x\/Hz(x, 3c)1/2 , where x is a nonzero vector in C and Hz is the Bergman metric on D . The number ßf(z) represents the maximum dilation of / at z . The set consisting of all ß/(z), for z e D and /: D —► A holomorphic, is known ...
متن کاملA Holomorphic Representation of the Jacobi Algebra
A representation of the Jacobi algebra h1 ⋊ su(1, 1) by first order differential operators with polynomial coefficients on the manifold C×D1 is presented. The Hilbert space of holomorphic functions on which the holomorphic first order differential operators with polynomials coefficients act is constructed.
متن کاملModerate Deviations for Martingales with Bounded Jumps
We prove that the Moderate Deviation Principle (MDP) holds for the trajectory of a locally square integrable martingale with bounded jumps as soon as its quadratic covariation, properly scaled, converges in probability at an exponential rate. A consequence of this MDP is the tightness of the method of bounded martingale differences in the regime of moderate deviations.
متن کاملConcentration Inequalities for Semi-bounded Martingales
In this paper we extend the results of de la Peña [3]. The main method that we use is the theory of decoupling, which has been developed in de la Peña [2] and [3]. Decoupling theory provides a general framework for analyzing problems involving dependent random variables as if they were independent. We will apply the theory of decoupling as in de la Peña [3] and some new inequalities for indepen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1982
ISSN: 0022-1236
DOI: 10.1016/0022-1236(82)90006-4