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1.
Goran Peskir 《Probability Theory and Related Fields》2002,124(1):100-111
Let (B
t
)
t
≥ 0) be a standard Brownian motion started at zero, let g : ℝ_+ →ℝ be an upper function for B satisfying g(0)=0, and let
be the first-passage time of B over g. Assume that g is C
1 on <0,∞>, increasing (locally at zero), and concave (locally at zero). Then the following identities hold for the density
function f of τ:
in the sense that if the second and third limit exist so does the first one and the equalities are valid (here is the standard normal density). These limits can take any value in [0,∞]. The method of proof relies upon the strong Markov
property of B and makes use of real analysis.
Received: 30 August 2001 / Revised version: 25 February 2002 / Published online: 22 August 2002 相似文献
2.
Summary. A turning-point theory is developed for the second-order difference equation
where the coefficients A
n
and B
n
have asymptotic expansions of the form
θ≠0 being a real number. In particular, it is shown how the Airy functions arise in the uniform asymptotic expansions of
the solutions to this three-term recurrence relation. As an illustration of the main result, a uniform asymptotic expansion
is derived for the orthogonal polynomials associated with the Freud weight exp(−x
4
), xℝ.
Received February 21, 2002 / Revised version received April 8, 2002 / Published online October 29, 2002
Mathematics Subject Classification (1991): 41A60, 39A10, 33C45
The work described in this paper was partially supported by a grant from the Research Grants Council of the Hong Kong Special
Administrative Region, China (Project No. CityU 1132 | 00P) 相似文献
3.
Let H be an infinite-dimensional real Hilbert space equipped with the scalar product (⋅,⋅)
H
. Let us consider three linear bounded operators,
We define the functions
where a
i
∈H and α
i
∈ℝ. In this paper, we discuss the closure and the convexity of the sets Φ
H
⊂ℝ2 and F
H
⊂ℝ3 defined by
Our work can be considered as an extension of Polyak’s results concerning the finite-dimensional case. 相似文献
4.
Cauchy problems for a second order linear differential operator equation
in a Hilbert space H are studied. Equations of this kind arise for example in elasticity and hydrodynamics. It is assumed that A
0 is a uniformly positive operator and that A
0−1/2
DA
0−1/2 is a bounded accretive operator in H. The location of the spectrum of the corresponding semigroup generator is described and sufficient conditions for analyticity
are given. 相似文献
5.
Ulrich Brehm 《Journal of Mathematical Sciences》2008,153(4):454-480
We show that under certain weak conditions on the module
R
M, every mapping
between the submodule lattices which preserves arbitrary joins and “disjointness” has a unique representation of the form
f(u) = 〈h[
S
B
R
×
R
U]〉 for all u ∈
, where
S
B
R
is some bimodule and h is an R-balanced mapping. Furthermore, f is a lattice homomorphism if and only if B
R
is flat and the induced S-module homomorphism
is monic. If
S
N also satisfies the same weak conditions, then f is a lattice isomorphism if and only if B
R
is a finitely generated projective generator, S ≅ End(B
R
) canonically, and
is an S-module isomorphism, i.e., every lattice isomorphism is induced by a Morita equivalence between R and S and a module isomorphism.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 46, Algebra,
2007. 相似文献
6.
Let B
H
and
be two independent, d-dimensional fractional Brownian motions with Hurst parameter H∈(0,1). Assume d≥2. We prove that the intersection local time of B
H
and
exists in L
2 if and only if Hd<2.
相似文献
7.
This paper studies products of Hankel operators on the Hardy space. We show thatH
f
(1)*
H
f(2)
H
f
(3)*
=0 for all permutation if and only if eitherH
f1 orH
f2 orH
f3 is zero. Using Douglas' localization theorem and Izuchi's theorem on Sarason's three functions problem, we show that
is a sufficient condition forH
f
*
H
g
H
h
*
,H
g
*
H
f
H
h
*
, andH
f
*
H
h
H
g
*
to be compact.This work was partly supported by NSF grants. The second author was also partly supported by the Research Council of Vanderbilt University. 相似文献
8.
Michal Vyroai 《Applications of Mathematics》2005,50(1):63-81
We consider a stochastic process X
t
x
which solves an equation
where A and are real matrices and BH is a fractional Brownian motion with Hurst parameter H (1/2,1). The Kolmogorov backward equation for the function u(t,x) =
f(X
t
x
) is derived and exponential convergence of probability distributions of solutions to the limit measure is established.This research has been supported by the grant no. 201/01/1197 of the Grant Agency of the Czech Republic.This revised version was published online in April 2005 with a corrected issue number. 相似文献
9.
Alessandro Zinani 《Monatshefte für Mathematik》2003,139(4):341-348
We calculate E[V
4(C)], the expected volume of a tetrahedron whose vertices are chosen randomly (i.e. independently and uniformly) in the interior of C, a cube of unit volume. We find
The result is in convincing agreement with a simulation of 3000·106 trials.Received February 12, 2002; in revised form August 13, 2002
Published online February 28, 2003 相似文献
10.
Tamás Erdélyi 《Mathematische Annalen》2003,326(3):489-498
Let P
n
(z)=∑
k=0
n
a
k,n
z
k
ℂ[z] be a sequence of unimodular polynomials (|a
k,n
|=1 for all k, n) which is ultraflat in the sense of Kahane, i.e.,
We prove the following conjecture of Queffelec and Saffari, see (1.30) in [QS2]. If q(0,∞) and (P
n
) is an ultraflat sequence of unimodular polynomials P
n
of degree n, then for f
n
(t):=Re(P
n
(e
it
)) we have
and
where Γ denotes the usual gamma function, and the ∼ symbol means that the ratio of the left and right hand sides converges
to 1 as . To this end we use results from [Er1] where we studied the structure of ultraflat polynomials and proved several conjectures
of Queffelec and Saffari.
Received: 9 September 2002 / Revised version: 1 November 2002 /
Published online: 8 April 2003
Mathematics Subject Classification (2000): 41A17
Research supported in part by the NSF of the USA under Grant No. Grant No. DMS–9623156 相似文献
11.
We analyse degenerate, second-order, elliptic operators H in divergence form on L
2(R
n
× R
m
). We assume the coefficients are real symmetric and a
1
H
δ
≥ H ≥ a
2
H
δ
for some a
1, a
2 > 0 where
Here x
1 ∈ R
n
, x
2 ∈ R
m
and are positive measurable functions such that behaves like as x → 0 and as with and . Our principal results state that the submarkovian semigroup is conservative and its kernel K
t
satisfies bounds
where |B(x; r)| denotes the volume of the ball B(x; r) centred at x with radius r measured with respect to the Riemannian distance associated with H. The proofs depend on detailed subelliptic estimations on H, a precise characterization of the Riemannian distance and the corresponding volumes and wave equation techniques which exploit
the finite speed of propagation. We discuss further implications of these bounds and give explicit examples that show the
kernel is not necessarily strictly positive, nor continuous. 相似文献
12.
We study the asymptotic behavior as n→∞ of the sequence
|
Sn=?i=0n-1K(naBH1i)(BH2i+1-BH2i)S_{n}=\sum_{i=0}^{n-1}K\bigl(n^{\alpha}B^{H_{1}}_{i}\bigr)\bigl(B^{H_{2}}_{i+1}-B^{H_{2}}_{i}\bigr) 相似文献
13.
Vincent Cachia Hagen Neidhardt Valentin A. Zagrebnov 《Integral Equations and Operator Theory》2001,39(4):396-412
We study the operator-norm error bound estimate for the exponential Trotter product formula in the case of accretive perturbations. LetA be a semibounded from below self-adjoint operator in a separable Hilbert space. LetB be a closed maximal accretive operator such that, together withB
*, they are Kato-small with respect toA with relative bounds less than one. We show that in this case the operator-norm error bound estimate for the exponential Trotter product formula is the same as for the self-adjointB [12]:
14.
Michael Bildhauer 《manuscripta mathematica》2003,110(3):325-342
Suppose that f: ℝ
nN
→ℝ is a strictly convex energy density of linear growth, f(Z)=g(|Z|2) if N>1. If f satisfies an ellipticity condition of the form
15.
CongWenLIU JiHuaiSHI 《数学学报(英文版)》2003,19(1):187-200
In 1993,Ahern,Flores and Rudin showed that,if f is integrable over the unit ball BC^n of C^n and satisfies∫BC^nfoφdv=f（φ（0)) for every φ∈Aut(BC^n),then f is M-harmonic if and only if n≤11.The present paper is about an analogous question in the context of the unit ball Bn of R^n as well as in the weighted setting. 相似文献
16.
In this paper, we show the equivalence of somequasi-random properties for sparse graphs, that is, graphsG with edge densityp=|E(G)|/(
2
n
)=o(1), whereo(1)→0 asn=|V(G)|→∞. Our main result (Theorem 16) is the following embedding result. For a graphJ, writeN
J(x) for the neighborhood of the vertexx inJ, and letδ(J) andΔ(J) be the minimum and the maximum degree inJ. LetH be atriangle-free graph and setd
H=max{δ(J):J⊆H}. Moreover, putD
H=min{2d
H,Δ(H)}. LetC>1 be a fixed constant and supposep=p(n)≫n
−1
D
H. We show that ifG is such that
17.
Hrvoje Šikić 《Journal of Theoretical Probability》2000,13(2):571-574
We prove that for a>0, (B
t) one-dimensional standard Brownian motion and
0=inf{t>0 : B
t=0} the following zero–one law is valid
18.
LetH be any complex inner product space with inner product <·,·>. We say thatf: ℂ→ℂ is Hermitian positive definite onH if the matrix
19.
20.
S. Mecheri 《Czechoslovak Mathematical Journal》2007,57(2):697-703
Let ℋ be a separable infinite dimensional complex Hilbert space, and let ℒ(H) denote the algebra of all bounded linear operators on ℋ into itself. Let A = (A
1, A
2,..., A
n), B = (B
1, B
2,..., B
n) be n-tuples of operators in ℒ(H); we define the elementary operators Δ
A,B
: ℒ(H) ↦ ℒ(H) by
|