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
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
基金supported by the National Key R&D Program of China(Grant No.2018YFA0703900)the National Natural Science Foundation of China(Grant No.11671231)+2 种基金the Qilu Young Scholars Program of Shandong Universitysupported by the Tian Yuan Projection of the National Natural Science Foundation of China(Grant Nos.11526205,11626247)the National Basic Research Program of China(973 Program)(Grant No.2007CB814900(Financial Risk)).
文摘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.
文摘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.