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1.
In this paper, we consider Beta(2−α,α)(2α,α) (with 1<α<21<α<2) and related ΛΛ-coalescents. If T(n)T(n) denotes the length of a randomly chosen external branch of the nn-coalescent, we prove the convergence of nα−1T(n)nα1T(n) when nn tends to ∞, and give the limit. To this aim, we give asymptotics for the number σ(n)σ(n) of collisions which occur in the nn-coalescent until the end of the chosen external branch, and for the block counting process associated with the nn-coalescent.  相似文献   

2.
Let EE be a Banach lattice and FF a Banach space. A bounded linear operator T:E→FT:EF is an isomorphism on the positive cone of EE if and only if TT is almost surjective. A dual version of this theorem holds also. A bounded linear operator T:F→ET:FE is almost surjective if and only if TT is an isomorphism on the positive cone of FF.  相似文献   

3.
Let x(s)x(s), s∈RdsRd be a Gaussian self-similar random process of index HH. We consider the problem of log-asymptotics for the probability pTpT that x(s)x(s), x(0)=0x(0)=0 does not exceed a fixed level in a star-shaped expanding domain T⋅ΔTΔ as T→∞T. We solve the problem of the existence of the limit, θ?lim(−logpT)/(logT)Dθ?lim(logpT)/(logT)D, T→∞T, for the fractional Brownian sheet x(s)x(s), s∈[0,T]2s[0,T]2 when D=2D=2, and we estimate θθ for the integrated fractional Brownian motion when D=1D=1.  相似文献   

4.
We show that if T:X→XT:XX is a continuous linear operator on an FF-space X≠{0}X{0}, then the set of frequently hypercyclic vectors of TT is of first category in XX, and this answers a question of A. Bonilla and K.-G. Grosse-Erdmann. We also show that if T:X→XT:XX is a bounded linear operator on a Banach space X≠{0}X{0} and if TT is frequently hypercyclic (or, more generally, syndetically transitive), then the TT-orbit of every non-zero element of XX is bounded away from 0, and in particular TT is not hypercyclic.  相似文献   

5.
By a perturbation method and constructing comparison functions, we reveal how the inhomogeneous term hh affects the exact asymptotic behaviour of solutions near the boundary to the problem △u=b(x)g(u)+λh(x)u=b(x)g(u)+λh(x), u>0u>0 in ΩΩ, u|Ω=∞u|Ω=, where ΩΩ is a bounded domain with smooth boundary in RNRN, λ>0λ>0, g∈C1[0,∞)gC1[0,) is increasing on [0,∞)[0,), g(0)=0g(0)=0, gg is regularly varying at infinity with positive index ρρ, the weight bb, which is non-trivial and non-negative in ΩΩ, may be vanishing on the boundary, and the inhomogeneous term hh is non-negative in ΩΩ and may be singular on the boundary.  相似文献   

6.
In this paper we establish the boundedness of the extremal solution uu in dimension N=4N=4 of the semilinear elliptic equation −Δu=λf(u)Δu=λf(u), in a general smooth bounded domain Ω⊂RNΩRN, with Dirichlet data u|Ω=0u|Ω=0, where ff is a C1C1 positive, nondecreasing and convex function in [0,∞)[0,) such that f(s)/s→∞f(s)/s as s→∞s.  相似文献   

7.
Let CC be a nonempty subset of a topological vector space EE. We state and prove new various fixed point theorems of Fan–Browder type for set-valued maps F:C→2EF:C2E such that C⊂F(C)CF(C) (called expansive), without assuming that the sets CC and F(C)F(C) are convex or compact or equal, and EE is Hausdorff. Let KK be a convex subset of EE and let CC be a nonempty subset of KK. Our proofs use a technique based on the investigations of the images of maps and restated for maps f:C×K→R∪{−∞,+∞}f:C×KR{,+} of G.X.-Z. Yuan’s results concerning the existence of equilibrium points and minimax inequalities for maps f:K×K→R∪{−∞,+∞}f:K×KR{,+}. Examples are provided.  相似文献   

8.
If U,VU,V are closed subspaces of a Fréchet space, then EE is the direct sum of UU and VV if and only if EE is the algebraic direct sum of the annihilators U°U° and V°V°. We provide a simple proof of this (possibly well-known) result.  相似文献   

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We prove that if for a continuous map ff on a compact metric space XX, the chain recurrent set, R(f)R(f) has more than one chain component, then ff does not satisfy the asymptotic average shadowing property. We also show that if a continuous map ff on a compact metric space XX has the asymptotic average shadowing property and if AA is an attractor for ff, then AA is the single attractor for ff and we have A=R(f)A=R(f). We also study diffeomorphisms with asymptotic average shadowing property and prove that if MM is a compact manifold which is not finite with dimM=2dimM=2, then the C1C1 interior of the set of all C1C1 diffeomorphisms with the asymptotic average shadowing property is characterized by the set of ΩΩ-stable diffeomorphisms.  相似文献   

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We derive a Molchan–Golosov-type integral transform which changes fractional Brownian motion of arbitrary Hurst index KK into fractional Brownian motion of index HH. Integration is carried out over [0,t][0,t], t>0t>0. The formula is derived in the time domain. Based on this transform, we construct a prelimit which converges in L2(P)L2(P)-sense to an analogous, already known Mandelbrot–Van Ness-type integral transform, where integration is over (−∞,t](,t], t>0t>0.  相似文献   

14.
For certain Gaussian processes X(t)X(t) with trend −ctβctβ and variance V2(t)V2(t), the ruin time is analyzed where the ruin time is defined as the first time point tt such that X(t)−ctβ≥uX(t)ctβu. The ruin time is of interest in finance and actuarial subjects. But the ruin time is also of interest in other applications, e.g. in telecommunications where it indicates the first time of an overflow. We derive the asymptotic distribution of the ruin time as u→∞u showing that the limiting distribution depends on the parameters ββ, V(t)V(t) and the correlation function of X(t)X(t).  相似文献   

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The oscillation of solutions of f+Af=0f+Af=0 is discussed by focusing on four separate situations. In the complex case AA is assumed to be either analytic in the unit disc DD or entire, while in the real case AA is continuous either on (−1,1)(1,1) or on (0,∞)(0,). In all situations AA is expected to grow beyond bounds that ensure finite oscillation for all (non-trivial) solutions, and the separation between distinct zeros of solutions is considered.  相似文献   

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We consider a multidimensional diffusion XX with drift coefficient b(Xt,α)b(Xt,α) and diffusion coefficient εa(Xt,β)εa(Xt,β) where αα and ββ are two unknown parameters, while εε is known. For a high frequency sample of observations of the diffusion at the time points k/nk/n, k=1,…,nk=1,,n, we propose a class of contrast functions and thus obtain estimators of (α,β)(α,β). The estimators are shown to be consistent and asymptotically normal when n→∞n and ε→0ε0 in such a way that ε−1n−ρε1nρ remains bounded for some ρ>0ρ>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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