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A universal robust limit theorem for nonlinear Lévy processes under sublinear expectation
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作者 Mingshang Hu Lianzi Jiang +1 位作者 Gechun Liang Shige Peng 《Probability, Uncertainty and Quantitative Risk》 2023年第1期1-32,共32页
This article establishes a universal robust limit theorem under a sublinear expectation framework.Under moment and consistency conditions,we show that,forα∈(1,2),the i.i.d.sequence{(1/√∑_(i=1)^(n)X_(i),1/n∑_(i=1)... This article establishes a universal robust limit theorem under a sublinear expectation framework.Under moment and consistency conditions,we show that,forα∈(1,2),the i.i.d.sequence{(1/√∑_(i=1)^(n)X_(i),1/n∑_(i=1)^(n)X_(i)Y_(i),1/α√n∑_(i=1)^(n)X_(i))}_(n=1)^(∞)converges in distribution to L_(1),where L_(t=(ε_(t),η_(t),ζ_(t))),t∈[0,1],is a multidimensional nonlinear Lévy process with an uncertainty■set as a set of Lévy triplets.This nonlinear Lévy process is characterized by a fully nonlinear and possibly degenerate partial integro-differential equation(PIDE){δ_(t)u(t,x,y,z)-sup_(F_(μ),q,Q)∈■{∫_(R^(d)δλu(t,x,y,z)(dλ)with.To construct the limit process,we develop a novel weak convergence approach based on the notions of tightness and weak compactness on a sublinear expectation space.We further prove a new type of Lévy-Khintchine representation formula to characterize.As a byproduct,we also provide a probabilistic approach to prove the existence of the above fully nonlinear degenerate PIDE. 展开更多
关键词 Universal robust limit theorem Partial integro-differential equation Nonlinear Lévy process α-stable distribution Sublinear expectation
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Fabrication of Polymeric Visual Decoys for the Male Emerald Ash Borer (Agrilus planipennis)
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作者 Drew P. Pulsifer Akhlesh Lakhtakia +5 位作者 Mahesh S. Narkhede Michael J. Domingue Beverly G. Post Jayant Kumar Raul J. Martln-Palma Thomas C. Baker 《Journal of Bionic Engineering》 SCIE EI CSCD 2013年第2期129-138,共10页
Through a bioreplication approach, we have fabricated artificial visual decoys for the invasive species Agrilus planipen- nis--commonly known as the Emerald Ash Borer (EAB). The mating behavior of this species invol... Through a bioreplication approach, we have fabricated artificial visual decoys for the invasive species Agrilus planipen- nis--commonly known as the Emerald Ash Borer (EAB). The mating behavior of this species involves an overflying EAB male pouncing on an EAB female at rest on an ash leaflet before copulating. The male spots the female on the leaflet by visually detecting the iridescent green color of the female's elytra. As rearing EAB and then deploying dead females as decoys for trapping is both arduous and inconvenient, we decided to fabricate artificial decoys. We used a dead female to make a negative die of nickel and a positive die of epoxy. Decoys were then made by first depositing a quarter-wave-stack Bragg reflector on a polymer sheet and then stamping it with a pair of matched negative and positive dies to take the shape of the upper surface of an EAB female. As nearly 100 artificial decoys were fabricated from just one EAB female, this bioreplication process is industrially scalable. Preliminary results from a field trapping test are indicative of success. 展开更多
关键词 bioreplication conformal-evaporated-film-by-rotation method ELECTROFORMING negative die positive die stampingCopyright ~ 2013 Jilin university. Published by Science Press and Elsevier Limited. All rights reserved.
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