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1.
We consider NN independent stochastic processes (Xj(t),t∈[0,T])(Xj(t),t[0,T]), j=1,…,Nj=1,,N, defined by a one-dimensional stochastic differential equation with coefficients depending on a random variable ?j?j and study the nonparametric estimation of the density of the random effect ?j?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 L2L2-risk. Asymptotic properties are evaluated as NN tends to infinity for fixed TT or for T=T(N)T=T(N) tending to infinity with NN. For T(N)=N2T(N)=N2, adaptive estimators are built. Estimators are implemented on simulated data for several examples.  相似文献   

2.
Let kk be a field of characteristic zero and RR a factorial affine kk-domain. Let BB be an affineRR-domain. In terms of locally nilpotent derivations, we give criteria for BB to be RR-isomorphic to the residue ring of a polynomial ring R[X1,X2,Y]R[X1,X2,Y] over RR by the ideal (X1X2−φ(Y))(X1X2φ(Y)) for φ(Y)∈R[Y]?Rφ(Y)R[Y]?R.  相似文献   

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In a rapidly growing population one expects that two individuals chosen at random from the nnth generation are unlikely to be closely related if nn 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}{pj} such that p0=0p0=0 and ψ(x)=jpjI{jx}ψ(x)=jpjI{jx} is asymptotic to x−αL(x)xαL(x) as x→∞x where L(⋅)L() is slowly varying at ∞ and 0<α<10<α<1 (and hence the mean m=∑jpj=∞m=jpj=) it is shown that if XnXn is the generation number of the coalescence of the lines of descent backwards in time of two randomly chosen individuals from the nnth generation then n−XnnXn converges in distribution to a proper distribution supported by N={1,2,3,…}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 mm satisfies 1<m≡∑jpj<∞1<mjpj< and p0=0p0=0 then coalescence time XnXn does converge to a proper distribution as n→∞n, i.e., coalescence does take place in the remote past.  相似文献   

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Consider events of the form {Zs≥ζ(s),s∈S}{Zsζ(s),sS}, where ZZ is a continuous Gaussian process with stationary increments, ζζ is a function that belongs to the reproducing kernel Hilbert space RR of process ZZ, and S⊂RSR is compact. The main problem considered in this paper is identifying the function β∈RβR satisfying β(s)≥ζ(s)β(s)ζ(s) on SS and having minimal RR-norm. The smoothness (mean square differentiability) of ZZ turns out to have a crucial impact on the structure of the solution. As examples, we obtain the explicit solutions when ζ(s)=sζ(s)=s for s∈[0,1]s[0,1] and ZZ is either a fractional Brownian motion or an integrated Ornstein–Uhlenbeck process.  相似文献   

6.
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   

7.
Let f:X→Yf:XY be a morphism between normal complex varieties, where YY is Kawamata log terminal. Given any differential form σσ, defined on the smooth locus of YY, we construct a “pull-back form” on XX. The pull-back map obtained by this construction is ?Y?Y-linear, uniquely determined by natural universal properties and exists even in cases where the image of ff is entirely contained in the singular locus of YY.  相似文献   

8.
Let ηtηt be a Poisson point process of intensity t≥1t1 on some state space YY and let ff be a non-negative symmetric function on YkYk for some k≥1k1. Applying ff to all kk-tuples of distinct points of ηtηt generates a point process ξtξt on the positive real half-axis. The scaling limit of ξtξt as tt tends to infinity is shown to be a Poisson point process with explicitly known intensity measure. From this, a limit theorem for the mm-th smallest point of ξtξt is concluded. This is strengthened by providing a rate of convergence. The technical background includes Wiener–Itô chaos decompositions and the Malliavin calculus of variations on the Poisson space as well as the Chen–Stein method for Poisson approximation. The general result is accompanied by a number of examples from geometric probability and stochastic geometry, such as kk-flats, random polytopes, random geometric graphs and random simplices. They are obtained by combining the general limit theorem with tools from convex and integral geometry.  相似文献   

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Consider a graph GG with a minimal edge cut FF and let G1G1, G2G2 be the two (augmented) components of G−FGF. A long-open question asks under which conditions the crossing number of GG is (greater than or) equal to the sum of the crossing numbers of G1G1 and G2G2—which would allow us to consider those graphs separately. It is known that crossing number is additive for |F|∈{0,1,2}|F|{0,1,2} and that there exist graphs violating this property with |F|≥4|F|4. In this paper, we show that crossing number is additive for |F|=3|F|=3, thus closing the final gap in the question.  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 αα is in (0,2)(0,2), equal to 2, and in (2,∞)(2,), respectively. The partial sum weakly converges to a functional of αα-stable process when α<2α<2 and converges to a functional of Brownian motion when α≥2α2. When the process is of short-memory and α<4α<4, the autocovariances converge to functionals of α/2α/2-stable processes; and if α≥4α4, they converge to functionals of Brownian motions. In contrast, when the process is of long-memory, depending on αα and ββ (the parameter that characterizes the long-memory), the autocovariances converge to either (i) functionals of α/2α/2-stable processes; (ii) Rosenblatt processes (indexed by ββ, 1/2<β<3/41/2<β<3/4); or (iii) functionals of Brownian motions. The rates of convergence in these limits depend on both the tail index αα 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][0,1] with either (i) the J1J1 or the M1M1 topology (Skorokhod, 1956); or (ii) the weaker form SS topology (Jakubowski, 1997). Some statistical applications are also discussed.  相似文献   

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This paper is concerned with the Cauchy problem for the fast diffusion equation ut−Δum=αup1utΔum=αup1 in RNRN (N≥1N1), where m∈(0,1)m(0,1), p1>1p1>1 and α>0α>0. The initial condition u0u0 is assumed to be continuous, nonnegative and bounded. Using a technique of subsolutions, we set up sufficient conditions on the initial value u0u0 so that u(t,x)u(t,x) blows up in finite time, and we show how to get estimates on the profile of u(t,x)u(t,x) for small enough values of t>0t>0.  相似文献   

18.
We show that the equality m1(f(x))=m2(g(x))m1(f(x))=m2(g(x)) for xx in a neighborhood of a point aa remains valid for all xx provided that ff and gg are open holomorphic maps, f(a)=g(a)=0f(a)=g(a)=0 and m1,m2m1,m2 are Minkowski functionals of bounded balanced domains. Moreover, a polynomial relation between ff and gg is obtained.  相似文献   

19.
The dynamic behaviour of the one-dimensional family of maps f(x)=c2[(a−1)x+c1]−λ/(α−1)f(x)=c2[(a1)x+c1]λ/(α1) is examined, for representative values of the control parameters a,c1a,c1, c2c2 and λλ. The maps under consideration are of special interest, since they are solutions of the relaxed Newton method derivative being equal to a constant aa. The maps f(x)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 xnxn versus λλ plot, an initial exponential decay followed by a bifurcation. The value of λλ at which this bifurcation takes place depends on the values of the parameters a,c1a,c1 and c2c2. This corresponds to a switch to an oscillatory behaviour with amplitudes of f(x)f(x) undergoing a period doubling. For values of aa higher than 1 and at higher values of λλ a reverse bifurcation occurs. The corresponding branches converge and a bleb is formed for values of the parameter c1c1 between 1 and 1.20. This behaviour is confirmed by calculating the corresponding Lyapunov exponents.  相似文献   

20.
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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