共查询到20条相似文献,搜索用时 15 毫秒
1.
A. D. Kolesnik 《Ukrainian Mathematical Journal》2008,60(12):1915-1926
A symmetric random evolution X(t) = (X
1 (t), …, X
m
(t)) controlled by a homogeneous Poisson process with parameter λ > 0 is considered in the Euclidean space ℝ
m
, m ≥ 2. We obtain an asymptotic relation for the transition density p(x, t), t > 0, of the process X(t) as λ → 0 and describe the behavior of p(x, t) near the boundary of the diffusion domain in spaces of different dimensions.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1631 – 1641, December, 2008. 相似文献
2.
MiaoLI QuanZHENG 《数学学报(英文版)》2004,20(5):821-828
Let T = (T(t))t≥0 be a bounded C-regularized semigroup generated by A on a Banach space X and R(C) be dense in X. We show that if there is a dense subspace Y of X such that for every x ∈ Y, σu(A, Cx), the set of all points λ ∈ iR to which (λ - A)^-1 Cx can not be extended holomorphically, is at most countable and σr(A) N iR = Ф, then T is stable. A stability result for the case of R(C) being non-dense is also given. Our results generalize the work on the stability of strongly continuous senfigroups. 相似文献
3.
Efstathios Paparoditis Dimitris N. Politis 《Annals of the Institute of Statistical Mathematics》2000,52(1):139-159
We consider the problem of estimating the distribution of a nonparametric (kernel) estimator of the conditional expectation g(x; ) = E((X
t+1) | Y
t,m
= x) of a strictly stationary stochastic process {X
t
, t 1}. In this notation (·) is a real-valued Borel function and Y
t,m
a segment of lagged values, i.e., Yt,m=(Xt-i
1,Xt-i
2,...,Xt-i
m), where the integers i
i
, satisfy 0 i12...m>. We show that under a fairly weak set of conditions on {X
t
, t 1}, an appropriately designed and simple bootstrap procedure that correctly imitates the conditional distribution of X
t+1 given the selective past Y
t,m
, approximates correctly the distribution of the class of nonparametric estimators considered. The procedure proposed is entirely nonparametric, its main dependence assumption refers to a strongly mixing process with a polynomial decrease of the mixing rate and it is not based on any particular assumptions on the model structure generating the observations. 相似文献
4.
Rong-mao ZHANG & Zheng-yan LIN Department of Mathematics Zhejiang University Hangzhou China 《中国科学A辑(英文版)》2007,50(1):35-46
Let {W(t),t∈R}, {B(t),t∈R } be two independent Brownian motions on R with W(0) = B(0) = 0. In this paper, we shall consider the exact Hausdorff measures for the image and graph sets of the d-dimensional iterated Brownian motion X(t), where X(t) = (Xi(t),... ,Xd(t)) and X1(t),... ,Xd(t) are d independent copies of Y(t) = W(B(t)). In particular, for any Borel set Q (?) (0,∞), the exact Hausdorff measures of the image X(Q) = {X(t) : t∈Q} and the graph GrX(Q) = {(t, X(t)) :t∈Q}are established. 相似文献
5.
Philippe et al. [9], [10] introduced two distinct time-varying mutually invertible fractionally integrated filters A(d), B(d) depending on an arbitrary sequence d = (d
t
)
t∈ℤ of real numbers; if the parameter sequence is constant d
t
≡ d, then both filters A(d) and B(d) reduce to the usual fractional integration operator (1 − L)−d
. They also studied partial sums limits of filtered white noise nonstationary processes A(d)ε
t
and B(d)ε
t
for certain classes of deterministic sequences d. The present paper discusses the randomly fractionally integrated stationary processes X
t
A
= A(d)ε
t
and X
t
B
= B(d)ε
t
by assuming that d = (d
t
, t ∈ ℤ) is a random iid sequence, independent of the noise (ε
t
). In the case where the mean
, we show that large sample properties of X
A
and X
B
are similar to FARIMA(0,
, 0) process; in particular, their partial sums converge to a fractional Brownian motion with parameter
. The most technical part of the paper is the study and characterization of limit distributions of partial sums for nonlinear
functions h(X
t
A
) of a randomly fractionally integrated process X
t
A
with Gaussian noise. We prove that the limit distribution of those sums is determined by a conditional Hermite rank of h. For the special case of a constant deterministic sequence d
t
, this reduces to the standard Hermite rank used in Dobrushin and Major [2].
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 1, pp. 3–28, January–March, 2007. 相似文献
6.
A one-term Edgeworth expansion for U-statistics with kernel h(x, y) was derived by Jing and Wang [3] under optimal moment conditions. In this note, we show that one of the optimal moment conditions
E| h(X
1, X
2|5/3 < ∞ can be weakened to lim
t→∞
t
5/3
P(|h(X
1, X
2)| > t) → 0.
Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 453–440, July–September, 2005. 相似文献
7.
Zhen-long Chen San-yang Liu 《应用数学学报(英文版)》2005,21(4):623-636
Let φ be a Hausdorff measure function and A be an infinite increasing sequence of positive integers. The Hausdorff-type measure φ - mA associated to φ and A is studied. Let X(t)(t ∈ R^N) be certain Gaussian random fields in R^d. We give the exact Hausdorff measure of the graph set GrX([0, 1]N), and evaluate the exact φ - mA measure of the image and graph set of X(t). A necessary and sufficient condition on the sequence A is given so that the usual Hausdorff measure function for X([0, 1] ^N) and GrX([0, 1]^N) are still the correct measure functions. If the sequence A increases faster, then some smaller measure functions will give positive and finite ( φ A)-Hausdorff measure for X([0, 1]^N) and GrX([0, 1]N). 相似文献
8.
We consider the M(t)/M(t)/m/m queue, where the arrival rate λ(t) and service rate μ(t) are arbitrary (smooth) functions of time. Letting pn(t) be the probability that n servers are occupied at time t (0≤ n≤ m, t > 0), we study this distribution asymptotically, for m→∞ with a comparably large arrival rate λ(t) = O(m) (with μ(t) = O(1)). We use singular perturbation techniques to solve the forward equation for pn(t) asymptotically. Particular attention is paid to computing the mean number of occupied servers and the blocking probability
pm(t). The analysis involves several different space-time ranges, as well as different initial conditions (we assume that at t = 0 exactly n0 servers are occupied, 0≤ n0≤ m). Numerical studies back up the asymptotic analysis.
AMS subject classification: 60K25,34E10
Supported in part by NSF grants DMS-99-71656 and DMS-02-02815 相似文献
9.
Let{(Xn, Yn)}n1 be a sequence of i.i.d. bi-variate vectors. In this article, we study the possible limit distributions ofU
n
h
(t), the so-calledconditional U-statistics, introduced by Stute.(10) They are estimators of functions of the formm
h
(t)=E{h(Y
1,...,Y
k
)|X
1=t
1,...,X
k
=t
k
},t=(t
1,...,t
k
)
k
whereE |h|<. Heret is fixed. In caset
1=...=tk=t (say), we describe the limiting random variables asmultiple Wiener integrals with respect toP
t, the conditional distribution ofY, givenX=t. Whent
i, 1ik, are not all equal, we introduce and use a slightly generalized version of a multiple Wiener integral.Research supported by National Board for Higher Mathematics, Bombay, India. 相似文献
10.
This paper concerns the abstract Cauchy problem (ACP) for an evolution equation of second order in time. LetA be a closed linear operator with domainD(A) dense in a Banach spaceX. We first characterize the exponential wellposedness of ACP onD(A
k+1),k teN. Next let {C(t);t teR} be a family of generalized solution operators, on [D(A
k)] toX, associated with an exponentially wellposed ACP onD(A
k+1). Then we define a new family {T(t); Ret>0} by the abstract Weierstrass formula. We show that {T(t)} forms a holomorphic semigroup of class (H
k) onX.
Research of the second-named author was partially supported by Grant-in-Aid for Scientific Research (No. 63540139), Ministry
of Education, Science and Culture. 相似文献
11.
Haruko Okamura 《Graphs and Combinatorics》2005,21(4):503-514
Let k≥2 be an integer and G = (V(G), E(G)) be a k-edge-connected graph. For X⊆V(G), e(X) denotes the number of edges between X and V(G) − X. Let {si, ti}⊆Xi⊆V(G) (i=1,2) and X1∩X2=∅. We here prove that if k is even and e(Xi)≤2k−1 (i=1,2), then there exist paths P1 and P2 such that Pi joins si and ti, V(Pi)⊆Xi (i=1,2) and G − E(P1∪P2) is (k−2)-edge-connected (for odd k, if e(X1)≤2k−2 and e(X2)≤2k−1, then the same result holds [10]), and we give a generalization of this result and some other results about paths not containing
given edges. 相似文献
12.
Let {X(t),t ∈ R+} be an integrated α stable process. In this paper, a functional law of the iterated logarithm (LIL) is derived via estimating the small ball probability of X. As a corollary,, the classical Chung LIL of X is obtained. Furthermore, some results about the weighted occupation measure of X(t) are established. 相似文献
13.
Fu Qing GAO 《数学学报(英文版)》2007,23(8):1527-1536
Let {Xn;n≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E(X1) and let {N(t); t ≥0} be a random process taking non-negative integer values with finite mean λ(t) = E(N(t)) and independent of {Xn; n ≥1}. In this paper, asymptotic expressions of P((X1 +… +XN(t)) -λ(t)μ 〉 x) uniformly for x ∈[γb(t), ∞) are obtained, where γ〉 0 and b(t) can be taken to be a positive function with limt→∞ b(t)/λ(t) = 0. 相似文献
14.
Simeon M. Berman 《纯数学与应用数学通讯》1990,43(5):575-598
Let X(t), t ≧ 0, be a Markov process in Rm with homogeneous transition density p(t; x, y). For a closed bounded set B ? Rm, X is said to have a self-intersection of order r ≧ 2 in B if there are distinct points t1 < … < tr such that X(t1) ∈ B and X(tj) = X(t1), for j = 2,…, r. The focus of this work is the Hausdorff measure, suitably defined, of the set of such r-tuples. The main result is that under general conditions on p(t; x, y) as well as the specific condition there is a measure function M(t), defined in terms of the integral above, such that the corresponding Hausdorff measure of self-intersection set is positive, with positive probability. The results are applied to Lévy and diffusion processes, and are shown to extend recent results in this area. 相似文献
15.
For a diffusion type process dXt = dWi + a(t, X)dt and a sequence (fn) of nonnegative functions necessary and sufficient conditions to the fn are established which guarantee the a.s. convergence of fn(Xt)dt to zero. This result is applied to derive simple necessary and sufficient conditions for the strong convergence of distributions of diffusion processes formulated in terms of the corresponding drift functions. 相似文献
16.
The bigraded Frobenius characteristic of the Garsia-Haiman module M
μ
is known [7, 10] to be given by the modified Macdonald polynomial [(H)\tilde]m[X; q, t]{\tilde{H}_{\mu}[X; q, t]}. It follows from this that, for
m\vdash n{\mu \vdash n} the symmetric polynomial ?p1 [(H)\tilde]m[X; q, t]{{\partial_{p1}} \tilde{H}_{\mu}[X; q, t]} is the bigraded Frobenius characteristic of the restriction of M
μ
from S
n
to S
n-1. The theory of Macdonald polynomials gives explicit formulas for the coefficients c
μ
v
occurring in the expansion ?p1 [(H)\tilde]m[X; q, t] = ?v ? mcmv [(H)\tilde]v[X; q, t]{{\partial_{p1}} \tilde{H}_{\mu}[X; q, t] = \sum_{v \to \mu}c_{\mu v} \tilde{H}_{v}[X; q, t]}. In particular, it follows from this formula that the bigraded Hilbert series F
μ (q, t) of M
μ
may be calculated from the recursion Fm (q, t) = ?v ? mcmv Fv (q, t){F_\mu (q, t) = \sum_{v \to \mu}c_{\mu v} F_v (q, t)}. One of the frustrating problems of the theory of Macdonald polynomials has been to derive from this recursion that Fm(q, t) ? N[q, t]{F\mu (q, t) \in \mathbf{N}[q, t]}. This difficulty arises from the fact that the c
μ
v
have rather intricate expressions as rational functions in q, t. We give here a new recursion, from which a new combinatorial formula for F
μ
(q, t) can be derived when μ is a two-column partition. The proof suggests a method for deriving an analogous formula in the general case. The method
was successfully carried out for the hook case by Yoo in [15]. 相似文献
17.
Joshua Rushton 《Journal of Theoretical Probability》2007,20(3):397-427
We establish a functional LIL for the maximal process M(t) :=sup 0≤s≤t
‖X(s)‖ of an ℝ
d
-valued α-stable Lévy process X, provided X(1) has density bounded away from zero over some neighborhood of the origin. We also provide a broad invariance result governing
a class independent-increment processes related to the domain of attraction of X(1). This breadth is particularly notable for two types of processes captured: First, it not only describes any partial sum
process built from iid summands in the domain of normal attraction of X(1), but also addresses those with arbitrary iid summands in the full domain of attraction (here we give a technical condition
necessary and sufficient for the partial sum process to share the exact LIL we prove for X). Second, it reveals that any Lévy process L such that L(1) satisfies the technical condition just mentioned will also share the LIL of X.
Supported in part by NSF Grant DMS 02-05034. 相似文献
18.
Let X(t) be an N parameter generalized Lévy sheet taking values in ℝd with a lower index α, ℜ = {(s, t] = ∏
i=1
N
(s
i, t
i], s
i < t
i}, E(x, Q) = {t ∈ Q: X(t) = x}, Q ∈ ℜ be the level set of X at x and X(Q) = {x: ∃t ∈ Q such that X(t) = x} be the image of X on Q. In this paper, the problems of the existence and increment size of the local times for X(t) are studied. In addition, the Hausdorff dimension of E(x, Q) and the upper bound of a uniform dimension for X(Q) are also established. 相似文献
19.
A. Díaz-Cano 《Journal of Pure and Applied Algebra》2001,160(2-3)
Let
be an analytic set germ of dimension 2. We study the invariant t(X0) defined as the least integer t such that any open semianalytic set germ of X0 can be written as a union of t basic open set germs. It is known that 2≤t(X0)≤3. In this note we provide a geometric criterion to determine the exact value of t(X0). 相似文献
20.
Dominique Arlettaz 《Central European Journal of Mathematics》2004,2(1):50-56
This paper provides universal upper bounds for the exponent of the kernel and of the cokernel of the classical Boardman homomorphism
b
n
: π
n
(X)→H
n
(H;ℤ), from the cohomotopy groups to the ordinary integral cohomology groups of a spectrum X, and of its various generalizations π
n
(X)→E
n
(X), F
n
(X)→(E∧F)
n
(X), F
n
(X)→H
n
(X;π
0
F) and F
n
(X)→H
n+t
(X;π
t
F) for other cohomology theories E
*(−) and F
*(−). These upper bounds do not depend on X and are given in terms of the exponents of the stable homotopy groups of spheres and, for the last three homomorphisms, in
terms of the order of the Postnikov invariants of the spectrum F. 相似文献