共查询到20条相似文献，搜索用时 453 毫秒
1.
WangWensheng 《高校应用数学学报(英文版)》2000,15(4):409-418
Let {W(t);t≥0} be a standard Brownian motion. For a positive integer m,define a Gaussian process Xm(t)=(1/m!)∫^1 0(t-s)^mdW(s). In this paper the liminf behavior of the increments of this process is discussed by establishing some probability inequalities. Some previous results are extended and improved. 相似文献
2.
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
3.
4.
Let be a real-valued fractional Brownian sheet. Consider the (N, d) Gaussian random field B
H
defined by
where are independent copies of B
0
H
. In this paper, the existence and joint continuity of the local times of B
H
are established.
Received: 2 October 2001 / Revised version: 7 January 2002 / Published online: 22 August 2002 相似文献
5.
Let B
0,B
1, ⋯ ,B
n
be independent standard Brownian motions, starting at 0. We investigate the tail of the capture time
where 0<b
i
≤ 1, 1 ≤i≤n. In particular, we have ?τ3=∞ and ?τ5<∞. Various generalizations are also studied.
Received: 10 January 2000 / Revised version: 12 January 2001 /?Published online: 14 June 2001 相似文献
6.
Let A = d/dθ denote the generator of the rotation group in the space C(Γ), where Γ denotes the unit circle. We show that the stochastic Cauchy problem
, where b is a standard Brownian motion and f ∈ C(Γ) is fixed, has a weak solution if and only if the stochastic convolution process t ↦ (f * b)t has a continuous modification, and that in this situation the weak solution has a continuous modification. In combination
with a recent result of Brzeźniak, Peszat and Zabczyk it follows that (1) fails to have a weak solution for all f ∈ C(Γ) outside a set of the first category. 相似文献
| ((1)) |
7.
Pietro Zamboni 《manuscripta mathematica》2000,102(3):311-323
In this note we prove the Harnack inequality for non negative solutions of the quasilinear equation
under very general structural assumptions satisfied by functions A and B.
Received: 25 March 1999/ Revised version: 18 February 2000 相似文献
8.
Let and be the von Mangoldt function and M?bius function, respectively, x real and y“small” compared with x. This paper gives, for the first time, a non-trivial estimate of the sum
for all whenever . Correspondingly, it is also proved that
uniformly for all real α and any , and in the same range of y.
Received 10 December 1996; in revised form 9 September 1997 相似文献
9.
E.G. Coffman Jr. George S. Lueker Joel Spencer Peter M. Winkler 《Probability Theory and Related Fields》2001,120(4):585-599
A random rectangle is the product of two independent random intervals, each being the interval between two random points
drawn independently and uniformly from [0,1]. We prove that te number C
n
of items in a maximum cardinality disjoint subset of n random rectangles satisfies
where K is an absolute constant. Although tight bounds for the problem generalized to d > 2 dimensions remain an open problem, we are able to show that, for some absolute constat K,
Finally, for a certain distribution of random cubes we show that for some absolute constant K, the number Q
n
of items in a maximum cardinality disjoint subset of the cubes satisies
Received: 1 September 1999 / Revised version: 3 November 2000 / Published online: 14 June 2001 相似文献
10.
Abstract. Weakly left ample semigroups are a class of semigroups that are (2,1) -subalgebras of semigroups of partial transformations, where the unary operation takes a transformation α to the identity map in the domain of α . It is known that there is a class of proper weakly left ample semigroups whose structure is determined by unipotent monoids acting on semilattices or categories. In
this paper we show that for every finite weakly left ample semigroup S , there is a finite proper weakly left ample semigroup
and an onto morphism from
to S which separates idempotents. In fact,
is actually a (2,1) -subalgebra of a symmetric inverse semigroup, that is, it is a left ample semigroup (formerly, left type A). 相似文献
11.
Yimin Xiao 《Journal of Theoretical Probability》1998,11(2):383-408
Let {W(t), tR} and {B(t), t0} be two independent Brownian motions in R with W(0) = B(0) = 0 and let
be the iterated Brownian motion. Define d-dimensional iterated Brownian motion by
where X
1, X
d are independent copies of Y. In this paper, we investigate the existence, joint continuity and Hölder conditions in the set variable of the local time
of X(t), where
is the Borel -algebra of R
+. These results are applied to study the irregularities of the sample paths and the uniform Hausdorff dimension of the image and inverse images of X(t). 相似文献
12.
Horst Alzer 《Monatshefte für Mathematik》2000,131(3):179-188
A classical inequality for Euler’s gamma function states that
for all and with . We prove the following extension of this result. Let be the weighted power mean of of order r. The inequality
holds for all and with if and only if
(Received 3 April 2000; in revised form 26 June 2000) 相似文献
13.
Let and be the von Mangoldt function and M?bius function, respectively, x real and y“small” compared with x. This paper gives, for the first time, a non-trivial estimate of the sum
for all whenever . Correspondingly, it is also proved that
相似文献
14.
It is well known that the recurrence relations
are periodic, in the sense that they define periodic sequences for all choices of the initial data, and lead to sequences
with periods 2, 5 and 8, respectively. In this paper we determine all periodic recursions of the form
where are complex numbers, are non-zero and . We find that, apart from the three recursions listed above, only
lead to periodic sequences (with periods 6 and 8). The non-periodicity of (R) when (or and ) depends on the connection between (R) and the recurrence relations
and
We investigate these recursions together with the related
Each of (A), (B), and (C) leads to periodic sequences if k = 1 (with periods 6, 5, and 9, respectively). Also, for k = 2, (B) leads to periodicity with period 8. However, no other cases give rise to periodicity. We also prove that every real
sequence satisfying any of (A), (B), and (C) must be bounded. As a consequence, we find that for an arbitrary k, every rational sequence satisfying any of (A), (B), and (C) must be periodic.
(Received 27 June 2000; in revised form 5 January 2001) 相似文献
15.
Global attractivity in a discrete delay logistic model 总被引：1，自引：0，他引：1
庾建设 《应用数学学报(英文版)》1998,14(1):80-85
1.IntroductionIntherecentworks[l--31,theauthorsconsideredthediscretedelaylogisticmodelIn[3],itwasshownthateverypositivesolutionof(l)oscillatesaboutitspositiveequilibriumx~(a--1)/0ifandonlyifIn[if(seealso[2]),itwasprovedthatiftheneverypositivesolutionof(1)tendstox~(or--1)/pasn-- co.Thepurposeofthispaperistoobtainanothersufficieatconditionforthepositiveequilibriumxof(1)tobeaglobalattractorbyusingamethodverydmerelltfromthatusedin[1,21.Themainresultofthispaperisthefollowingtheorem.*Thisworkispart… 相似文献
16.
Viorel Barbu Aurel Răşcanu Gianmario Tessitore 《Applied Mathematics and Optimization》2003,47(2):97-120
Abstract. This work is concerned with Carleman inequalities and controllability properties for the following stochastic linear heat
equation (with Dirichlet boundary conditions in the bounded domain D
⊂ R
d
and multiplicative noise):
and for the corresponding backward dual equation:
We prove the null controllability of the backward equation and obtain partial results for the controllability of the forward
equation.
\par 相似文献
17.
J. Schoißengeier 《Monatshefte für Mathematik》2000,131(3):227-234
For a real number x let be the fractional part of x and for any set M let c
M
be the characteristic function of M. For and a positive integer N let
be the discrepancy of the sequence modulo 1. In this paper we prove that
(Received 2 May 2000; in revised form 19 June 2000) 相似文献
18.
The Stokes lines/curves are identified for the Mittag—Leffler function
When α is not real, it is found that the Stokes curves are spirals. Away from the Stokes lines/curves, exponentially improved uniform
asymptotic expansions are obtained. Near the Stokes lines/curves, Berry-type smooth transitions are achieved via the use of
the complementary error function. 相似文献
19.
Micciancio 《Discrete and Computational Geometry》2003,29(1):133-138
Abstract. We prove that the best way to reduce the volume of the n -dimensional unit cube by a linear transformation that maps each of the main vertices
to a point within distance ɛ <
from
is to shorten all edges by a factor (1-ɛ) . In particular, the minimal volume of such an almost cubic parallelepiped is (1-ɛ)
n
. This problem naturally arises in the construction of lattice-based one-way functions with worst-case/ average-case connection. 相似文献
20.
Geometric Properties of Fractional Brownian Sheets 总被引：1，自引：1，他引：0
Let
be an (N, d)-fractional Brownian sheet with Hurst index H = (H1,...,HN) ∈ (0, 1)N. Our objective of the present article is to characterize the anisotropic nature of BH in terms of H. We prove the following results: (1) BH is sectorially locally nondeterministic. (2) By introducing a notion of "dimension" for Borel measures and sets, which is
suitable for describing the anisotropic nature of BH, we determine
for an arbitrary Borel set
Moreover, when Bα is an (N, d)-fractional Brownian sheet with index 〈α〉 = (α,..., α) (0 < α < 1), we prove the following uniform Hausdorff
dimension result for its image sets: If N ≤ αd, then with probability one,
(3) We provide sufficient conditions for the image BH(E) to be a Salem set or to have interior points. The results in (2) and (3) describe the geometric and Fourier analytic properties
of BH. They extend and improve the previous theorems of Mountford [35], Khoshnevisan and Xiao [29] and Khoshnevisan, Wu, and Xiao
[28] for the Brownian sheet, and Ayache and Xiao [5] for fractional Brownian sheets. 相似文献