منابع مشابه
Note on Radial Dunkl Processes
This note encloses relatively short proofs of the following known results: the radial Dunkl process associated with a reduced system and a strictly positive multiplicity function is the unique strong solution for all time t of a stochastic differential equation of a singular drift (see [12] for the original proof and [4] for a proof under additional restrictions), the first hitting time of the ...
متن کاملRadial Dunkl Processes Associated with Dihedral Systems
We give some interest in radial Dunkl processes associated with dihedral systems. We write down the semi group density and as a by-product the generalized Bessel function and the W -invariant generalized Hermite polynomials. Then, a skew product decomposition, involving only independent Bessel processes, is given and the tail distribution of the first hitting time of boundary of the Weyl chambe...
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This paper reports preliminary progress on a principled approach to modelling nonstationary phenomena using neural networks. We are concerned with both parameter and model order complexity estimation. The basic methodology assumes a Bayesian foundation. However t o allow the construction of pragmatic models, successive approximations have to be made l o permit computational tractibility. The lo...
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In this paper we present a radial basis function based extension to a recently proposed variational algorithm for approximate inference for diffusion processes. Inference, for state and in particular (hyper-) parameters, in diffusion processes is a challenging and crucial task. We show that the new radial basis function approximation based algorithm converges to the original algorithm and has b...
متن کاملRadial Dunkl Processes : Existence and Uniqueness , Hitting Time , Beta Processes and Random Matrices
Abstract. We begin with the study of some properties of the radial Dunkl process associated to a reduced root system R. It is shown that this diffusion is the unique strong solution for all t ≥ 0 of a SDE with singular drift. Then, we study T0, the first hitting time of the positive Weyl chamber : we prove, via stochastic calculus, a result already obtained by Chybiryakov on the finiteness of T...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1973
ISSN: 0091-1798
DOI: 10.1214/aop/1176996890