共查询到20条相似文献,搜索用时 15 毫秒
1.
George Haiman 《Stochastic Processes and their Applications》1999,80(2):231-248
For a 1-dependent stationary sequence {Xn} we first show that if u satisfies p1=p1(u)=P(X1>u)0.025 and n>3 is such that 88np131, thenwhere withandFrom this result we deduce, for a stationary T-dependent process with a.s. continuous path {Ys}, a similar, in terms of P{max0skTYs<u}, k=1,2 formula for P{max0stYsu}, t>3T and apply this formula to the process Ys=W(s+1)−W(s), s0, where {W(s)} is the Wiener process. We then obtain numerical estimations of the above probabilities. 相似文献
P{max(X1,…,Xn)u}=ν·μn+O{p13(88n(1+124np13)+561)}, n>3,
ν=1−p2+2p3−3p4+p12+6p22−6p1p2,μ=(1+p1−p2+p3−p4+2p12+3p22−5p1p2)−1
pk=pk(u)=P{min(X1,…,Xk)>u}, k1
|O(x)||x|.
2.
R. A. Kasonga 《Stochastic Processes and their Applications》1988,30(2):263-275
Consider the following Itô stochastic differential equation dX(t) = ƒ(θ0, X(t)) dt + dW(t), where (W(t), t 0), is a standard Wiener process in RN. On the basis of discrete data 0 = t0 < t1 < …<tn = T; X(t1),...,X(tn) we would like to estimate the parameter θ0. We shall define the least squares estimator
and show that under some regularity conditions,
is strongly consistent. 相似文献
3.
We study the problem of selecting one of the r best of n rankable individuals arriving in random order, in which selection must be made with a stopping rule based only on the relative ranks of the successive arrivals. For each r up to r=25, we give the limiting (as n→∞) optimal risk (probability of not selecting one of the r best) and the limiting optimal proportion of individuals to let go by before being willing to stop. (The complete limiting form of the optimal stopping rule is presented for each r up to r=10, and for r=15, 20 and 25.) We show that, for large n and r, the optical risk is approximately (1−t*)r, where t*≈0.2834 is obtained as the roof of a function which is the solution to a certain differential equation. The optimal stopping rule τr,n lets approximately t*n arrivals go by and then stops ‘almost immediately’, in the sense that τr,n/n→t* in probability as n→∞, r→∞ 相似文献
4.
A note on geometric ergodicity of autoregressive conditional heteroscedasticity (ARCH) model 总被引:1,自引:0,他引:1
Zudi Lu 《Statistics & probability letters》1996,30(4):305-311
For the pth-order linear ARCH model, , where 0 > 0, i 0, I = 1, 2, …, p, {t} is an i.i.d. normal white noise with Et = 0, Et2 = 1, and t is independent of {Xs, s < t}, Engle (1982) obtained the necessary and sufficient condition for the second-order stationarity, that is, 1 + 2 + ··· + p < 1. In this note, we assume that t has the probability density function p(t) which is positive and lower-semicontinuous over the real line, but not necessarily Gaussian, then the geometric ergodicity of the ARCH(p) process is proved under Et2 = 1. When t has only the first-order absolute moment, a sufficient condition for the geometric ergodicity is also given. 相似文献
5.
Oscillation theorems for second-order half-linear differential equations 总被引:11,自引:0,他引:11
Oscillation criteria for the second-order half-linear differential equation are established, where > 0 is a constant and
exists for t [t0, ∞). We apply these results to the following equation: where
, D = (D1,…, DN), Ωa = x
N : |x| ≥ a} is an exterior domain, and c C([a, ∞),
), n > 1 and N ≥ 2 are integers. Here, a > 0 is a given constant. 相似文献
[r(t)|ξ′(t)|−1 ξ′(t)]′ + p(t)|ξ(t)|−1ξ(t)=0, t t0
6.
We have considered the problem of the weak convergence, as tends to zero, of the multiple integral processesin the space
, where fL2([0,T]n) is a given function, and {η(t)}>0 is a family of stochastic processes with absolutely continuous paths that converges weakly to the Brownian motion. In view of the known results when n2 and f(t1,…,tn)=1{t1<t2<<tn}, we cannot expect that these multiple integrals converge to the multiple Itô–Wiener integral of f, because the quadratic variations of the η are null. We have obtained the existence of the limit for any {η}, when f is given by a multimeasure, and under some conditions on {η} when f is a continuous function and when f(t1,…,tn)=f1(t1)fn(tn)1{t1<t2<<tn}, with fiL2([0,T]) for any i=1,…,n. In all these cases the limit process is the multiple Stratonovich integral of the function f. 相似文献
7.
We investigate multiplicity of solutions u(x, t) for a piecewise linear perturbation −(bu+−au−) of the one-dimensional beam operator utt + uxxx under Dirichlet boundary condition on the interval (fr|Sol|π/2,π/2) π/2) and periodic codition on the vasible t. Our concern is to investigate multiplicity of solutions of the equation when the nonlinearity crosses finite eigenvalues and the source term is generated by two eigenfunctions. 相似文献
8.
At time tk, a unit with magnitude Xk and lifetime Lk enters a system. Let λ be a real valued function on the finite real sequences. One such sequence, B*t, consists of the Xk's for which tk t < tk + Lk. When λ(X1,…, Xn) converges (in some sense) to φ, we find conditions under which λ(B*t) converges or fails to converge to φ in the same sense. 相似文献
9.
Liudas Giraitis Donatas Surgailis 《Stochastic Processes and their Applications》2002,100(1-2):275-300
We discuss the covariance structure and long-memory properties of stationary solutions of the bilinear equation Xt=ζtAt+Bt,(), where
are standard i.i.d. r.v.'s, and At,Bt are moving averages in Xs, s<t. Stationary solution of () is obtained as an orthogonal Volterra expansion. In the case At≡1, Xt is the classical AR(∞) process, while Bt≡0 gives the LARCH model studied by Giraitis et al. (Ann. Appl. Probab. 10 (2000) 1002). In the general case, Xt may exhibit long memory both in conditional mean and in conditional variance, with arbitrary fractional parameters
and
, respectively. We also discuss the hyperbolic decay of auto- and/or cross-covariances of Xt and Xt2 and the asymptotic distribution of the corresponding partial sums’ processes. 相似文献
10.
Aihua Fan 《Stochastic Processes and their Applications》2000,90(2):263-275
Given an infinite sequence t=(k)k of −1 and +1, we consider the oriented walk defined by Sn(t)=∑k=1n12…k. The set of t's whose behaviors satisfy Sn(t)bnτ is considered (
and 0<τ1 being fixed) and its Hausdorff dimension is calculated. A two-dimensional model is also studied. A three-dimensional model is described, but the problem remains open. 相似文献
11.
U. G. Abdullaev 《Applied Mathematics Letters》1994,7(6):85-89
We consider the nonlinear parabolic equation ut = (k(u)ux)x + b(u)x, where u = u(x, t, x ε R1, t > 0; k(u) ≥ 0, b(u) ≥ 0 are continuous functions as u ≥ 0, b (0) = 0; k, b > 0 as u > 0. At t = 0 nonnegative, continuous and bounded initial value is prescribed. The boundary condition u(0, t) = Ψ(t) is supposed to be unbounded as t → +∞. In this paper, sufficient conditions for space localization of unbounded boundary perturbations are found. For instance, we show that nonlinear equation ut = (unux)x + (uβ)x, n ≥ 0, β >; n + 1, exhibits the phenomenon of “inner boundedness,” for arbitrary unbounded boundary perturbations. 相似文献
12.
Michael A. Kouritzin 《Stochastic Processes and their Applications》1995,60(2):343-353
Suppose {k, −∞ < k < ∞} is an independent, not necessarily identically distributed sequence of random variables, and {cj}∞j=0, {dj}∞j=0 are sequences of real numbers such that Σjc2j < ∞, Σjd2j < ∞. Then, under appropriate moment conditions on {k, −∞ < k < ∞}, yk Σ∞j=0cjk-j, zk Σ∞j=0djk-j exist almost surely and in
4 and the question of Gaussian approximation to S[t]Σ[t]k=1 (yk zk − E{yk zk}) becomes of interest. Prior to this work several related central limit theorems and a weak invariance principle were proven under stationary assumptions. In this note, we demonstrate that an almost sure invariance principle for S[t], with error bound sharp enough to imply a weak invariance principle, a functional law of the iterated logarithm, and even upper and lower class results, also exists. Moreover, we remove virtually all constraints on k for “time” k ≤ 0, weaken the stationarity assumptions on {k, −∞ < k < ∞}, and improve the summability conditions on {cj}∞j=0, {dj}∞j=0 as compared to the existing weak invariance principle. Applications relevant to this work include normal approximation and almost sure fluctuation results in sample covariances (let dj = cj-m for j ≥ m and otherwise 0), quadratic forms, Whittle's and Hosoya's estimates, adaptive filtering and stochastic approximation. 相似文献
13.
We present a characterization of those Euclidean distance matrices (EDMs) D which can be expressed as D=λ(E−C) for some nonnegative scalar λ and some correlation matrix C, where E is the matrix of all ones. This shows that the coneswhere
is the elliptope (set of correlation matrices) and
is the (closed convex) cone of EDMs.we havefor some scalar independent of i. 相似文献
The characterization is given using the Gale transform of the points generating D. We also show that given points , for any scalars λ1,λ2,…,λn such that
∑j=1nλjpj=0, ∑j=1nλj=0,
∑j=1nλjpi−pj2= forall i=1,…,n,
14.
J. Gao 《Applied Mathematics Letters》2004,17(12):1381-1386
Let X be a Banach space, S(X) - x ε X : #x02016; = 1 be the unit sphere of X.The parameter, modulus of W*-convexity, W*(ε) = inf <(x − y)/2, fx> : x, y S(X), x − y ≥ ε, fx Δx , where 0 ≤ ε ≤ 2 and Δx S(X*) be the set of norm 1 supporting functionals of S(X) at x, is investigated_ The relationship among uniform nonsquareness, uniform normal structure and the parameter W*(ε) are studied, and a known result is improved. The main result is that for a Banach space X, if there is ε, where 0 < ε < 1/2, such that W*(1 + ε) > ε/2 where W*(1 + ε) = lim→ε W* (1 + ), then X has normal structure. 相似文献
15.
Mark J. Kaiser 《Computational Geometry》1999,12(3-4):177-217
The mixed volume optimization problem is to determine the point of duality Q for a given convex set K that minimizes the “mixed volume” of the associated polar set (K*;Q). In the plane, the mixed volumes translate as the area and length; in space, the mixed volumes include the volume, surface area, and mean width. In this paper, the geometric optimization problems associated with minimizing mixed volumes are examined from two perspectives: enumerative search and symbolic computation. The problem of minimizing the polar area through an enumerative search is first considered. The dual polygon (Pm*;Q) is constructed for an arbitrary point of duality QPm° by using an algebraic correspondence between the edges of Pm and the vertices of (Pm*;Q), and the area of (Pm*;Q), A(P*m;Q), is calculated and minimized using naive search techniques. A result due to Santaló is applied to verify the minimizing solution, and computational tests are described for various classes of randomly generated polygons. Statistical evidence indicates that a “good” approximation to the minimum area polar polygon occurs when the duality point is located at the center-of-gravity of Pm. The polar area problem is then investigated using symbolic procedures. Explicit symbolic expressions for the polar area and length functionals are computed and solved directly using the differential optimality conditions and Newton's iterative method of solution. The mixed volume and surface area functionals are formulated and solved using numerical products, and the mean width functional is described. Examples are used throughout to illustratethe methodology. 相似文献
16.
A mapping ƒ : n=1∞In → I is called a bag mapping having the self-identity if for every (x1,…,xn) ε i=1∞In we have (1) ƒ(x1,…,xn) = ƒ(xi1,…,xin) for any arrangement (i1,…,in) of {1,…,n}; monotonic; (3) ƒ(x1,…,xn, ƒ(x1,…,xn)) = ƒ(x1,…,xn). Let {ωi,n : I = 1,…,n;n = 1,2,…} be a family of non-negative real numbers satisfying Σi=1nωi,n = 1 for every n. Then one calls the mapping ƒ : i=1∞In → I defined as follows an OWA bag mapping: for every (x1,…,xn) ε i=1∞In, ƒ(x1,…,xn) = Σi=1nωi,nyi, where yi is the it largest element in the set {x1,…,xn}. In this paper, we give a sufficient and necessary condition for an OWA bag mapping having the self-identity. 相似文献
17.
A polynomial in two variables is defined by Cn(x,t)=ΣπΠnx(Gπ,x)t|π|, where Πn is the lattice of partitions of the set {1, 2, …, n}, Gπ is a certain interval graph defined in terms of the partition gp, χ(Gπ, x) is the chromatic polynomial of Gπ and |π| is the number of blocks in π. It is shown that , where S(n, i) is the Stirling number of the second kind and (x)i = x(x − 1) ··· (x − i + 1). As a special case, Cn(−1, −t) = An(t), where An(t) is the nth Eulerian polynomial. Moreover, An(t)=ΣπΠnaπt|π| where aπ is the number of acyclic orientations of Gπ. 相似文献
18.
G. D. Dietz 《Applied Mathematics Letters》2002,15(8):945-953
Let W be an n-dimensional vector space over a field F; for each positive integer m, let the m-tuples (U1, …, Um) of vector subspaces of W be uniformly distributed; and consider the statistics Xm,1 dimF(∑i=1m Ui) and Xm,2 dimF (∩i=1m Ui). If F is finite of cardinality q, we determine lim E(Xm,1k), and lim E(Xm,2k), and hence, lim var(Xm,1) and lim var(Xm,2), for any k > 0, where the limits are taken as q → ∞ (for fixed n). Further, we determine whether these, and other related, limits are attained monotonically. Analogous issues are also addressed for the case of infinite F. 相似文献
19.
A q × n array with entries from 0, 1,…,q − 1 is said to form a difference matrix if the vector difference (modulo q) of each pair of columns consists of a permutation of [0, 1,… q − 1]; this definition is inverted from the more standard one to be found, e.g., in Colbourn and de Launey (1996). The following idea generalizes this notion: Given an appropriate δ (-[−1, 1]t, a λq × n array will be said to form a (t, q, λ, Δ) sign-balanced matrix if for each choice C1, C2,…, Ct of t columns and for each choice = (1,…,t) Δ of signs, the linear combination ∑j=1t jCj contains (mod q) each entry of [0, 1,…, q − 1] exactly λ times. We consider the following extremal problem in this paper: How large does the number k = k(n, t, q, λ, δ) of rows have to be so that for each choice of t columns and for each choice (1, …, t) of signs in δ, the linear combination ∑j=1t jCj contains each entry of [0, 1,…, q t- 1] at least λ times? We use probabilistic methods, in particular the Lovász local lemma and the Stein-Chen method of Poisson approximation to obtain general (logarithmic) upper bounds on the numbers k(n, t, q, λ, δ), and to provide Poisson approximations for the probability distribution of the number W of deficient sets of t columns, given a random array. It is proved, in addition, that arithmetic modulo q yields the smallest array - in a sense to be described. 相似文献
20.
Nicolas Lichiardopol 《Discrete Mathematics》2004,280(1-3):119-131
In 1996, J.C. Bermond, T. Kodate, S. Perennes and N. Marlin conjectured that the set Fσ of fixed points of some complete rotation σ of the toroidal mesh TM(p)k is not separating (that is Fσ does not disconnect TM(p)k). They also conjectured that the set Fω of fixed points of any complete rotation ω of any Cayley digraph is not separating. In this paper, we prove the first conjecture and disprove the second one. 相似文献