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We first study L6vy measures, Poisson and Gaussian convolution semigroups on commutative hypergroups. Then we present a Lbvy-Khintchine type representation of a convolution semigroup (pJ,,, with sy...
We study continuous additive functionals of zero quadratic variation of strong Markov continuous local martingales by means of stochastic calculus. We show that they admit a representation as a sto...
Let D be a nonempty open bounded subset of d 2 2, and let 0 < a c 2. For a-harmonic functions on D vanishing outside D an analogue of the Martin representation for harmonic functions is derived.
A variational representation for positive functionals of a Hilbert space valued Wiener process (w(.)is) p roved. This representation is then used to prove a large deviations principle for the family...
The paper deals with continuous Banach-space-valued stationary random processes on linear spaces. From von Waldenfels' 1131 integral representation of positive definite functions on a linear space ...
For a nice Markov process such as Brownian motion on a domain in Rd, we prove a representation of excessive functions in terms of expected suprema This is motivated by recent work of El Karoui [S] ...
We consider the classification problem on the cube $[0,1]^d$ when the Bayes rule is known to belong to some new functions classes. These classes are made of prediction rules satisfying some conditions...
We show how the Clark-Ocone-Haussmann formula for Brownian motion on a compact Riemannian manifold put forward by S. Fang in his proof of the spectral gap inequality for the Ornstein-Uhlenbeck operato...
We define a sequence of mappings $Gamma_k:D_0(R_+)^kto D_0(R_+)^k$ and prove the following result: Let $N_1,ldots,N_n$ be the counting functions of independent Poisson processes on $R_+$ with respecti...
We study some probabilistic representations, based on branching processes, of a simple nonlinear differential equation, i.e. $u'=lambda u(au^R-1)$. The first approach is basically the same used by Le ...
We study some probabilistic representations, based on branching processes, of a simple nonlinear differential equation, i.e. $u'=lambda u(au^R-1)$. The first approach is basically the same used by Le ...
We derive a unified stochastic picture for the duality of a resampling-selection model with a branching-coalescing particle process (cf. MR2123250) and for the self-duality of Feller's branching diffu...
We derive a unified stochastic picture for the duality of a resampling-selection model with a branching-coalescing particle process (cf. MR2123250) and for the self-duality of Feller's branching diffu...
Some statistics in common use take a form of a ratio of two statistics such as sample correlation coefficient, Pearson’s coefficient of variation and so on. In this paper, obtaining an asymptotic repr...
Suppose the data consist of a set S of points xj , 1 ≤ j ≤ J, distributed in a bounded domain D RN, where N is a large number. An algorithm is given for finding the sets Lk of dimension k N, k = 1, ...

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