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ON THE STRUCTURES OF random measure AND POINT PROCESS CONVOLUTION SEMIGROUPS

Chinese Annals of Mathematics,Series B 1996年第4期17卷 467-476页

作者：何远江中山大学数学系广东广州

Let D be a convolution semigroup of random measures or point processes on a locally compact second countable T 2space. There is a topological isomorphism from D into a subsemigroup of product topological semigroup (R +,+) N.D is a sequentially stable and D-separable ZH-semigroup, as well as a metrizable, stable and normable Hun semigroup, so it has the corresponding properties. In particular the author has a new and simple proof byZH-semigroup approach or Hun semigroup approach to show that D has property ILID (an infinitesimal array limit is infinitely divisible), and know the Baire types which some subsets of D belong in.

关键词： random measure Point process ZH-semigroup Hun semigroup Property ILID

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MULTIFRACTAL DECOMPOSITION OF CERTAIN RECURSIVE SETS WITHOUT THE OPEN SET CONDITION

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Acta Mathematica Scientia 2001年第3期21卷 369-374页

作者：郭红文邓爱娇 Department of Mathematics Wuhan University Wuhan 430071 China Department of Mathematics Henan Normal University

The open set condition is the weakest condition hitherto in multifractal decomposition on the recursive sets. This paper deals with certain recursive fractals which have no relevence to the separation condition and gi... 详细信息

关键词： random measure multifractal dimension

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Backward Doubly Stochastic Differential Equations with Jumps and Stochastic Partial Differential-Integral Equations

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Chinese Annals of Mathematics,Series B 2012年第1期33卷 127-142页

作者： Qingfeng ZHU Yufeng SHI School of Mathematics Shandong UniversityJinan 250100China School of Statistics and Mathematics Shandong University of Finance and EconomicsJinan 250014China School of Mathematics Shandong UniversityJinan 250100China

Backward doubly stochastic differential equations driven by Brownian motions and Poisson process （BDSDEP） with non-Lipschitz coefficients on random time interval are studied. The probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential-integral equations （SPDIEs） is treated with BDSDEP. Under non-Lipschitz conditions, the existence and uniqueness results for measurable solutions to BDSDEP are established via the smoothing technique. Then, the continuous depen- dence for solutions to BDSDEP is derived. Finally, the probabilistic interpretation for the solutions to a class of quasilinear SPDIEs is given.

关键词： Backward doubly stochastic differential equations Stochastic partialdifferential-integral equations random measure Poisson process

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Detecting the filamentary structure of 3D point clouds:Proposal of a wavelet-based method

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International Journal of Modeling, Simulation, and Scientific Computing 2017年第3期8卷 311-336页

作者： Roberto D’Ercole Department of Biomedical and Clinical Sciences“L.Sacco”University of Milan Via G.B.Grassi 74 Milan 20157Italy

The analysis of the filamentary structure of the cosmo as well as that of the internal structure of the polar ice suggests the development of models based on three-dimensional(3D)point processes.A point process,regarded as a random measure,can be expressed as a sum of Delta Dirac measures concentrated at some random *** integration with respect to the point process leads the continuous wavelet transform of the process *** possible mother wavelets,we propose the application of the Mexican hat and the Morlet wavelet in order to implement the scale-angle energy density of the process,depending on the dilation parameter and on the three angles which define the direction in the Euclidean *** indicator proves to be a sensitive detector of any variation in the direction and it can be successfully implemented to study the isotropy or the filamentary structure in 3D point patterns.

关键词： 3D Continuous wavelet transform energy density scale-angle energy density Mexican hat Morlet mother wavelet random measure filamentary structure rotation matrix Euler angles isotropy anisotropy

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Hölder Continuity of Solutions of SPDEs with Reflection

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Communications in Mathematics and Statistics 2013年第2期1卷 133-142页

作者： Robert C.Dalang Tusheng Zhang Institut de Mathématiques Ecole Polytechnique Fédérale de LausanneStation 81015 LausanneSwitzerland School of Mathematics University of ManchesterOxford RoadManchester M139PLEnglandUK

In this paper,we obtain the Hölder continuity of the solutions of SPDEs with reflection,which have singular drifts(random measures).

关键词： Parabolic obstacle problem Stochastic partial differential equations with reflection random measure Garsia’s lemma

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