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We consider N independent stochastic processes (Xj(t),t∈[0,T]), j=1,…,N, defined by a one-dimensional stochastic differential equation with coefficients depending on a random variable ?j and study the nonparametric estimation of the density of the random effect ?j in two kinds of mixed models. A multiplicative random effect and an additive random effect are successively considered. In each case, we build kernel and deconvolution estimators and study their L2-risk. Asymptotic properties are evaluated as N tends to infinity for fixed T or for T=T(N) tending to infinity with N. For T(N)=N2, adaptive estimators are built. Estimators are implemented on simulated data for several examples. 相似文献
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In a rapidly growing population one expects that two individuals chosen at random from the nth generation are unlikely to be closely related if n is large. In this paper it is shown that for a broad class of rapidly growing populations this is not the case. For a Galton–Watson branching process with an offspring distribution {pj} such that p0=0 and ψ(x)=∑jpjI{j≥x} is asymptotic to x−αL(x) as x→∞ where L(⋅) is slowly varying at ∞ and 0<α<1 (and hence the mean m=∑jpj=∞) it is shown that if Xn is the generation number of the coalescence of the lines of descent backwards in time of two randomly chosen individuals from the nth generation then n−Xn converges in distribution to a proper distribution supported by N={1,2,3,…}. That is, in such a rapidly growing population coalescence occurs in the recent past rather than the remote past. We do show that if the offspring mean m satisfies 1<m≡∑jpj<∞ and p0=0 then coalescence time Xn does converge to a proper distribution as n→∞, i.e., coalescence does take place in the remote past. 相似文献
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We consider a multidimensional diffusion X with drift coefficient b(α,Xt) and diffusion coefficient ?σ(β,Xt). The diffusion sample path is discretely observed at times tk=kΔ for k=1…n on a fixed interval [0,T]. We study minimum contrast estimators derived from the Gaussian process approximating X for small ?. We obtain consistent and asymptotically normal estimators of α for fixed Δ and ?→0 and of (α,β) for Δ→0 and ?→0 without any condition linking ? and Δ. We compare the estimators obtained with various methods and for various magnitudes of Δ 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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This paper considers the short- and long-memory linear processes with GARCH (1,1) noises. The functional limit distributions of the partial sum and the sample autocovariances are derived when the tail index α is in (0,2), equal to 2, and in (2,∞), respectively. The partial sum weakly converges to a functional of α-stable process when α<2 and converges to a functional of Brownian motion when α≥2. When the process is of short-memory and α<4, the autocovariances converge to functionals of α/2-stable processes; and if α≥4, they converge to functionals of Brownian motions. In contrast, when the process is of long-memory, depending on α and β (the parameter that characterizes the long-memory), the autocovariances converge to either (i) functionals of α/2-stable processes; (ii) Rosenblatt processes (indexed by β, 1/2<β<3/4); or (iii) functionals of Brownian motions. The rates of convergence in these limits depend on both the tail index α and whether or not the linear process is short- or long-memory. Our weak convergence is established on the space of càdlàg functions on [0,1] with either (i) the J1 or the M1 topology (Skorokhod, 1956); or (ii) the weaker form S topology (Jakubowski, 1997). Some statistical applications are also discussed. 相似文献
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Consider a graph G with a minimal edge cut F and let G1, G2 be the two (augmented) components of G−F. A long-open question asks under which conditions the crossing number of G is (greater than or) equal to the sum of the crossing numbers of G1 and G2—which would allow us to consider those graphs separately. It is known that crossing number is additive for |F|∈{0,1,2} and that there exist graphs violating this property with |F|≥4. In this paper, we show that crossing number is additive for |F|=3, thus closing the final gap in the question. 相似文献
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Let k be a field of characteristic zero and R a factorial affine k-domain. Let B be an affineR-domain. In terms of locally nilpotent derivations, we give criteria for B to be R-isomorphic to the residue ring of a polynomial ring R[X1,X2,Y] over R by the ideal (X1X2−φ(Y)) for φ(Y)∈R[Y]?R. 相似文献
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Paul-Emile Maing 《Nonlinear Analysis: Theory, Methods & Applications》2008,68(12):3913-3922
This paper is concerned with the Cauchy problem for the fast diffusion equation ut−Δum=αup1 in RN (N≥1), where m∈(0,1), p1>1 and α>0. The initial condition u0 is assumed to be continuous, nonnegative and bounded. Using a technique of subsolutions, we set up sufficient conditions on the initial value u0 so that u(t,x) blows up in finite time, and we show how to get estimates on the profile of u(t,x) for small enough values of t>0. 相似文献
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In this note we study distance-regular graphs with a small number of vertices compared to the valency. We show that for a given α>2, there are finitely many distance-regular graphs Γ with valency k, diameter D≥3 and v vertices satisfying v≤αk unless (D=3 and Γ is imprimitive) or (D=4 and Γ is antipodal and bipartite). We also show, as a consequence of this result, that there are finitely many distance-regular graphs with valency k≥3, diameter D≥3 and c2≥εk for a given 0<ε<1 unless (D=3 and Γ is imprimitive) or (D=4 and Γ is antipodal and bipartite). 相似文献
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Let k be any field, G be a finite group acting on the rational function field k(xg:g∈G) by h⋅xg=xhg for any h,g∈G. Define k(G)=k(xg:g∈G)G. Noether’s problem asks whether k(G) is rational (= purely transcendental) over k. A weaker notion, retract rationality introduced by Saltman, is also very useful for the study of Noether’s problem. We prove that, if G is a Frobenius group with abelian Frobenius kernel, then k(G) is retract k-rational for any field k satisfying some mild conditions. As an application, we show that, for any algebraic number field k, for any Frobenius group G with Frobenius complement isomorphic to SL2(F5), there is a Galois extension field K over k whose Galois group is isomorphic to G, i.e. the inverse Galois problem is valid for the pair (G,k). The same result is true for any non-solvable Frobenius group if k(ζ8) is a cyclic extension of k. 相似文献
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For s≥3 a graph is K1,s-free if it does not contain an induced subgraph isomorphic to K1,s. Cycles in K1,3-free graphs, called claw-free graphs, have been well studied. In this paper we extend results on disjoint cycles in claw-free graphs satisfying certain minimum degree conditions to K1,s-free graphs, normally called generalized claw-free graphs. In particular, we prove that if G is K1,s-free of sufficiently large order n=3k with δ(G)≥n/2+c for some constant c=c(s), then G contains k disjoint triangles. Analogous results with the complete graph K3 replaced by a complete graph Km for m≥3 will be proved. Also, the existence of 2-factors for K1,s-free graphs with minimum degree conditions will be shown. 相似文献
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Bosek and Krawczyk exhibited an on-line algorithm for partitioning an on-line poset of width w into w14lgw chains. They also observed that the problem of on-line chain partitioning of general posets of width w could be reduced to First-Fit chain partitioning of 2w2+1-ladder-free posets of width w, where an m-ladder is the transitive closure of the union of two incomparable chains x1≤?≤xm, y1≤?≤ym and the set of comparabilities {x1≤y1,…,xm≤ym}. Here, we provide a subexponential upper bound (in terms of w with m fixed) for the performance of First-Fit chain partitioning on m-ladder-free posets, as well as an exact quadratic bound when m=2, and an upper bound linear in m when w=2. Using the Bosek–Krawczyk observation, this yields an on-line chain partitioning algorithm with a somewhat improved performance bound. More importantly, the algorithm and the proof of its performance bound are much simpler. 相似文献
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Let K be a closed convex subset of a q-uniformly smooth separable Banach space, T:K→K a strictly pseudocontractive mapping, and f:K→K an L-Lispschitzian strongly pseudocontractive mapping. For any t∈(0,1), let xt be the unique fixed point of tf+(1-t)T. We prove that if T has a fixed point, then {xt} converges to a fixed point of T as t approaches to 0. 相似文献
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We consider a multidimensional diffusion X with drift coefficient b(Xt,α) and diffusion coefficient εa(Xt,β) where α and β are two unknown parameters, while ε is known. For a high frequency sample of observations of the diffusion at the time points k/n, k=1,…,n, we propose a class of contrast functions and thus obtain estimators of (α,β). The estimators are shown to be consistent and asymptotically normal when n→∞ and ε→0 in such a way that ε−1n−ρ remains bounded for some ρ>0. The main focus is on the construction of explicit contrast functions, but it is noted that the theory covers quadratic martingale estimating functions as a special case. In a simulation study we consider the finite sample behaviour and the applicability to a financial model of an estimator obtained from a simple explicit contrast function. 相似文献
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We show that the equality m1(f(x))=m2(g(x)) for x in a neighborhood of a point a remains valid for all x provided that f and g are open holomorphic maps, f(a)=g(a)=0 and m1,m2 are Minkowski functionals of bounded balanced domains. Moreover, a polynomial relation between f and g is obtained. 相似文献
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Mehmet Özer Yasar Polatoglu Gürsel Hacibekiroglou Antonios Valaristos Amalia N. Miliou Antonios N. Anagnostopoulos Antanas Čenys 《Nonlinear Analysis: Theory, Methods & Applications》2008
The dynamic behaviour of the one-dimensional family of maps f(x)=c2[(a−1)x+c1]−λ/(α−1) is examined, for representative values of the control parameters a,c1, c2 and λ. The maps under consideration are of special interest, since they are solutions of the relaxed Newton method derivative being equal to a constant a. The maps f(x) are also proved to be solutions of a non-linear differential equation with outstanding applications in the field of power electronics. The recurrent form of these maps, after excessive iterations, shows, in an xn versus λ plot, an initial exponential decay followed by a bifurcation. The value of λ at which this bifurcation takes place depends on the values of the parameters a,c1 and c2. This corresponds to a switch to an oscillatory behaviour with amplitudes of f(x) undergoing a period doubling. For values of a higher than 1 and at higher values of λ a reverse bifurcation occurs. The corresponding branches converge and a bleb is formed for values of the parameter c1 between 1 and 1.20. This behaviour is confirmed by calculating the corresponding Lyapunov exponents. 相似文献