共查询到20条相似文献,搜索用时 31 毫秒
1.
G. S. Watson 《Annals of the Institute of Statistical Mathematics》1986,38(1):263-275
Summary We consider distributions with densities of the formf(μ′x) andf(‖x
v
‖) where μ andx are unit vectors inR
q
and ‖x
v
‖ is the norm of the part ofx in somes dimensional subspaceV ofR
q
. For several loss functions, optimal Bayesian and Pitman estimators of μ andV are given. When uniform priors are used, these estimators are identical. Then the infinitesimal robustness characteristics
of several special cases of these estimators are calculated. 相似文献
2.
Consider the retarded difference equationx
n
−x
n−1
=F(−f(x
n
)+g(x
n−k
)), wherek is a positive integer,F,f,g:R→R are continuous,F andf are increasing onR, anduF(u)>0 for allu≠0. We show that whenf(y)≥g(y) (resp. f(y)≤g(y)) fory∈R, every solution of (*) tends to either a constant or −∞ (resp. ∞) asn→∞. Furthermore, iff(y)≡g(y) fory∈R, then every solution of (*) tends to a constant asn→∞.
Project supported by NNSF (19601016) of China and NSF (97-37-42) of Hunan 相似文献
3.
Suppose thatA ⊂R
n
is a bounded set of diameter 1 and that:f:A →l
2 is a map satisfying the nearisometry condition |x−y|−ɛ≤|fx−fy|≤|x−y|+ɛ withɛ≤1. Then there is an isometryS:A →l
2 such that |Sx−fx|≤c
n √ɛ for allx inA. IfA satisfies a thickness condition and iff:A →R
n
, then there is an isometryS:R
n
→R
n
with |Sx−fx|≤c
nɛ/q, whereq is a thickness parameter. 相似文献
4.
I. Kh. Khusnullin 《Computational Mathematics and Mathematical Physics》2010,50(4):646-664
A perturbed two-parameter boundary value problem is considered for a second-order differential operator on an interval with
Dirichlet conditions. The perturbation is described by the potential μ−1
V((x − x
0)ɛ−1), where 0 < ɛ ≪ 1 and μ is an arbitrary parameter such that there exists δ > 0 for which ɛ/μ = o(ɛδ). It is shown that the eigenvalues of this operator converge, as ɛ → 0, to the eigenvalues of the operator with no potential.
Complete asymptotic expansions of the eigenvalues and eigenfunctions of the perturbed operator are constructed. 相似文献
5.
A sequence (μ
n) of probability measures on the real line is said to converge vaguely to a measureμ if∫ fdμ
n →∫ fdμ for every continuous functionf withcompact support. In this paper one investigates problems analogous to the classical central limit problem under vague convergence.
Let ‖μ‖ denote the total mass ofμ andδ
0 denote the probability measure concentrated in the origin. For the theory of infinitesimal triangular arrays it is true in
the present context, as it is in the classical one, that all obtainable limit laws are limits of sequences of infinitely divisible
probability laws. However, unlike the classical situation, the class of infinitely divisible laws is not closed under vague
convergence. It is shown that for every probability measureμ there is a closed interval [0,λ], [0,e
−1] ⊂ [0,λ] ⊂ [0, 1], such thatβμ is attainable as a limit of infinitely divisible probability laws iffβ ε [0,λ]. In the independent identically distributed case, it is shown that if (x
1 + ... +x
n)/a
n, an → ∞, converges vaguely toμ with 0<‖μ‖<1, thenμ=‖μ‖δ
0. If furthermore the ratiosa
n+1/a
n are bounded above and below by positive numbers, thenL(x)=P[|X
1|>x] is a slowly varying function ofx. Conversely, ifL(x) is slowly varying, then for everyβ ε (0, 1) one can choosea
n → ∞ so that the limit measure=βδ
0.
To the memory of Shlomo Horowitz
This research was partially supported by the National Science Foundation. 相似文献
6.
Let T:x↦2x (mod 1) be the doubling map of the circle ?=ℝ/ℤ. We construct a trigonometric polynomial f:?→ℝ with the following property: ∫f
dμ≥0 for every T-invariant probability measure μ, so that f is cohomologous to a non-negative Lipschitz function, yet f is not cohomologous to any non-negative C
1 function.
Oblatum 28-VI-2001 & 4-X-2001?Published online: 18 January 2002 相似文献
7.
Let ξ,ξ
1,ξ
2,… be positive i.i.d. random variables, S=∑
j=1∞
a(j)ξ
j
, where the coefficients a(j)≥0 are such that P(S<∞)=1. We obtain an explicit form of the asymptotics of −ln P(S<x) as x→0 for the following three cases:
The research partially supported by the RFBR grants 05-01-00810 and 06-01-00738, the Russian President’s grant NSh-8980-2006.1,
and the INTAS grant 03-51-5018. The second author also supported by the Lavrentiev SB RAS grant for young scientists. 相似文献
(i) | the sequence {a(j)} is regularly varying with exponent −β<−1, and −ln P(ξ<x)=O(x −γ+δ ) as x→0 for some δ>0, where γ=1/(β−1), |
(ii) | −ln P(ξ<x) is regularly varying with exponent −γ<0 as x→0, and a(j)=O(j −β−δ ) as j→∞ for some δ>0, where γ=1/(β−1), |
(iii) | {a(j)} decreases faster than any power of j, and P(ξ<x) is regularly varying with positive exponent as x→0. |
8.
Věra Trnková 《Applied Categorical Structures》2007,15(5-6):621-631
Solving the problem stated in Sichler and Trnková, Topol. Its Appl., 142: 159–179, 2004, we construct metrics μ, ν on a set P such that the spaces X=(P,μ) and Y=(P,ν) have the same monoid of all continuous selfmaps, the space Y is coconnected (in the sense that every continuous map Y×Y→Y depends on at most one coordinate) while X is not. Also, properties of the forgetful functors Metr → Unif → Top are investigated for the “simultaneous variant” of the
above problem.
Supported by the Grant Agency of Czech Republic under grant 201/06/0664 and by the project of Ministry of Education of Czech
Republic MSM 0021620839. 相似文献
9.
Marco Antei 《Israel Journal of Mathematics》2011,186(1):427-446
Let S be a connected Dedekind scheme and X an S-scheme provided with a section x. We prove that the morphism between fundamental group schemes π
1(X, x)
ab
→ π
1(Alb
X/S
, 0AlbX/S{0_{{\rm{Al}}{{\rm{b}}_{X/S}}}}) induced by the canonical morphism from X to its Albanese scheme Alb
X/S
(when the latter exists) fits in an exact sequence of group schemes 0 → (NS
X/S
τ
)⋎ → π
1(X, x)
ab
→ π
1(Alb
X/S
, 0AlbX/S{0_{{\rm{Al}}{{\rm{b}}_{X/S}}}}) → 0, where the kernel is a finite and flat S-group scheme. Furthermore, we prove that any finite and commutative quotient pointed torsor over the generic fiber X
η
of X can be extended to a finite and commutative pointed torsor over X. 相似文献
10.
Stefan Eilertsen 《Arkiv f?r Matematik》2000,38(1):53-75
A sufficient condition for the Wiener regularity of a boundary point with respect to the operator (− Δ)μ inR
n
,n≥1, is obtained, for μ∈(0,1/2n)/(1,1/2n−1). This extends some results for the polyharmonic operator obtained by Maz'ya and Maz'ya-Donchev.
As in the polyharmonic case, the proof is based on a weighted positivity property of (− Δ)μ, where the weight is a fundamental solution of this operator. It is shown that this property holds for μ as above while there
is an interval [A
n
, 1/2n−A
n
], whereA
n
→1, asn→∞, with μ-values for which the property does not hold. This interval is non-empty forn≥8. 相似文献
11.
Let (G, χ, x) be a triple consisting of a finitely presented groupG, epimorphism χ:G →Z, and distinguished elementx ∈G such that χ(x)=1. Given a finite symmetric groupS
r, we construct a finite directed graph Γ that describes the set Φ
r
of representations π: Ker χ →S
r as well as the mapping σ
x
:Φ
r
→Φ
r
defined by (σ
x
ϱ)(a) = ϱ(x
−1
ax) for alla ∈ Ker χ. The pair (Φ
r
,σ
x
has the structure of a shift of finite type, a well-known type of compact 0-dimensional dynamical system. We discuss basic
properties and applications of therepresentation shift (Φ
r
,σ
x
), including applications to knot theory. 相似文献
12.
Ishai Oren 《Israel Journal of Mathematics》1982,42(4):353-360
LetT be the unit circle, α irrational andF: T → R a step function. A necessary and sufficient condition for the skew of the α-rotation byf (considered as taking values mod 1) to be minimal is given. Also, the boundedness of Σ
i=1
n
f(x+iα asn → α is resolved. 相似文献
13.
Kazuhiro Takimoto 《Calculus of Variations and Partial Differential Equations》2006,26(3):357-377
We consider the boundary blowup problem for k-curvature equation, i.e., H
k
[u] = f(u) g(|Du|) in an n-dimensional domain Ω, with the boundary condition u(x) → ∞ as dist (x,∂Ω) → 0. We prove the existence result under some hypotheses. We also establish the asymptotic behavior of a solution near the boundary ∂Ω.
Mathematics Subject Classification (2000) 35J65, 35B40, 53C21 相似文献
14.
Let μ and ν be probability measures on a group Γ and let G
μ
and G
ν
denote Green’s function with respect to μ and ν. The group Γ is said to admit instability of Green’s function if there are symmetric, finitely supported measures μ and ν and a sequence {x
n
} such that G
μ
(e, x
n
)/G
ν
(e,x
n
) →0, and Γ admits instability of recurrence if there is a set S that is recurrent with respect to ν but transient with respect to μ. We give a number of examples of groups that have the Liouville property but have both types of instabilities. Previously
known groups with these instabilities did not have the Liouville property. 相似文献
15.
D. S. Lubinsky 《Constructive Approximation》2011,34(3):357-369
Let μ be a compactly supported positive measure on the real line, with associated Christoffel functions λ
n
(d
μ,⋅). Let g be a measurable function that is bounded above and below on supp[μ] by positive constants. We show that λ
n
(g
d
μ,⋅)/λ
n
(d
μ,⋅)→g in measure in {x:μ′(x)>0} and consequently in all L
p
norms, p<∞. The novelty is that there are no local or global restrictions on μ. The main idea is a new maximal function estimate for the “tail” in Nevai’s operators. 相似文献
16.
Let με be invariant measures of the Markov chainsx
n
F
which are small random perturbations of an endomorphismf of the interval [0,1] satisfying the conditions of Misiurewicz [6]. It is shown here that in the ergodic case με converges as ε→0 to the smoothf-invariant measure which exists according to [6]. This result exhibits the first example of stability with respect to random
perturbations while stability with respect to deterministic perturbations does not take place. 相似文献
17.
In this article we study the exponential behavior of the continuous stochastic Anderson model, i.e. the solution of the stochastic
partial differential equation u(t,x)=1+∫0tκΔxu (s,x) ds+∫0t W(ds,x) u (s,x), when the spatial parameter x is continuous, specifically x∈R, and W is a Gaussian field on R+×R that is Brownian in time, but whose spatial distribution is widely unrestricted. We give a partial existence result of the
Lyapunov exponent defined as limt→∞t−1 log u(t,x). Furthermore, we find upper and lower bounds for lim supt→∞t−1 log u(t,x) and lim inft→∞t−1 log u(t,x) respectively, as functions of the diffusion constant κ which depend on the regularity of W in x. Our bounds are sharper, work for a wider range of regularity scales, and are significantly easier to prove than all previously
known results. When the uniform modulus of continuity of the process W is in the logarithmic scale, our bounds are optimal.
This author's research partially supported by NSF grant no. : 0204999 相似文献
18.
Olivier Guibé 《Annali di Matematica Pura ed Applicata》2002,180(4):441-449
We give a partial uniqueness result concerning comparable renormalized solutions of the nonlinear elliptic problem -div(a(x,Du))=μ in Ω, u=0 on ∂Ω, where μ is a Radon measure with bounded variation on Ω.
Received: December 27, 2000 Published online: December 19, 2001 相似文献
19.
Byungdo Kim 《数学学报(英文版)》2000,16(1):21-28
Abstract
Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A→A such that [D(x), x]D(x)[D(x),x] ∈ rad(A) for all x∈A. In this case, D(A) ⊆ rad (A).
The author has been supported by Kangnung National University, Research Fund, 1998 相似文献
20.
Wei-hua Yang 《应用数学学报(英文版)》2006,22(4):687-702
In this paper, we consider the Neumann boundary value problem for a system of two elliptic equations involving the critical Sobolev exponents. By means of blowing-up method, we obtain behavior of positives with low energy and asymptotic behavior of positive solutions with minimum energy as the parameters λ,μ→∞. 相似文献