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We consider a multidimensional diffusion XX with drift coefficient b(α,Xt)b(α,Xt) and diffusion coefficient ?σ(β,Xt)?σ(β,Xt). The diffusion sample path is discretely observed at times tk=kΔtk=kΔ for k=1…nk=1n on a fixed interval [0,T][0,T]. We study minimum contrast estimators derived from the Gaussian process approximating XX for small ??. We obtain consistent and asymptotically normal estimators of αα for fixed ΔΔ and ?→0?0 and of (α,β)(α,β) for Δ→0Δ0 and ?→0?0 without any condition linking ?? and ΔΔ. We compare the estimators obtained with various methods and for various magnitudes of ΔΔ and ?? based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework.  相似文献   

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A net (xα)(xα) in a vector lattice X   is said to be unbounded order convergent (or uo-convergent, for short) to x∈XxX if the net (|xα−x|∧y)(|xαx|y) converges to 0 in order for all y∈X+yX+. In this paper, we study unbounded order convergence in dual spaces of Banach lattices. Let X   be a Banach lattice. We prove that every norm bounded uo-convergent net in X?X? is w?w?-convergent iff X   has order continuous norm, and that every w?w?-convergent net in X?X? is uo-convergent iff X is atomic with order continuous norm. We also characterize among σ  -order complete Banach lattices the spaces in whose dual space every simultaneously uo- and w?w?-convergent sequence converges weakly/in norm.  相似文献   

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Let KK be a closed convex subset of a qq-uniformly smooth separable Banach space, T:K→KT:KK a strictly pseudocontractive mapping, and f:K→Kf:KK an LL-Lispschitzian strongly pseudocontractive mapping. For any t∈(0,1)t(0,1), let xtxt be the unique fixed point of tf+(1-t)Ttf+(1-t)T. We prove that if TT has a fixed point, then {xt}{xt} converges to a fixed point of TT as tt approaches to 0.  相似文献   

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In this paper, we prove a kind of Abelian theorem for a class of stochastic volatility models (X,V)(X,V) where both the state process XX and the volatility process VV may have jumps. Our results relate the asymptotic behavior of the characteristic function of XΔXΔ for some Δ>0Δ>0 in a stationary regime to the Blumenthal–Getoor indexes of the Lévy processes driving the jumps in XX and VV. The results obtained are used to construct consistent estimators for the above Blumenthal–Getoor indexes based on low-frequency observations of the state process XX. We derive convergence rates for the corresponding estimator and show that these rates cannot be improved in general.  相似文献   

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Suppose XX is a real qq-uniformly smooth Banach space and F,K:X→XF,K:XX are Lipschitz ??-strongly accretive maps with D(K)=F(X)=XD(K)=F(X)=X. Let uu denote the unique solution of the Hammerstein equation u+KFu=0u+KFu=0. An iteration process recently introduced by Chidume and Zegeye is shown to converge strongly to uu. No invertibility assumption is imposed on KK and the operators KK and FF need not be defined on compact subsets of XX. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included.  相似文献   

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We show that for each p∈(0,1]p(0,1] there exists a separable p  -Banach space GpGp of almost universal disposition, that is, having the following extension property: for each ε>0ε>0 and each isometric embedding g:X→Yg:XY, where Y is a finite-dimensional p-Banach space and X   is a subspace of GpGp, there is an ε  -isometry f:Y→Gpf:YGp such that x=f(g(x))x=f(g(x)) for all x∈XxX.  相似文献   

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