共查询到20条相似文献,搜索用时 31 毫秒
1.
Jürg Hüsler 《Stochastic Processes and their Applications》1979,8(3):315-321
Let {Kk,k∈Z} be a stationary, normalized Gaussian sequence and define τβ=min(k:Xk>?βk} the first crossing point of the Gaussian sequence with the moving boundary ?βt. For β→0 we discuss in this paper the a.s. stability, the a.s. relative ability of τβ and an iterated logarithm law for τβ, depending on the correlation function. 相似文献
2.
Let {δt}t>0 be a non-isotropic dilation group on R n . Let τ: R n → [0,∞) be a continuous function that vanishes only at the origin and satisfies τ(δ t x) = tτ(x), t > 0, x ∈ R n . In this paper we obtain two-sided inequalities for spherical means of the form $\int_{S^{n-1}}\tau(r_1\omega_1,\cdots,r_n\omega_n)^{-\alpha}d\sigma (\omega),$ where α is a positive constant, and r1,…, rn are positive parameters. 相似文献
3.
Sun-Wah Kiu 《Stochastic Processes and their Applications》1980,10(2):183-191
A Markov process in Rn{xt} with transition function Pt is called semi-stable of order α>0 if for every a>0, Pt(x, E) = Pat(aax, aaE). Let ?t(ω)=∫t0|xs(ω)|-1/α ds, T(t) be its inverse and {yt}={xT(t)}.Theorem 1: {Yt} is a multiplicative invariant process; i.e., it has transition function qt satisfying qt(x,E)=qt(ax,aE) for all a > 0.Theorem 2: If {xt} is Feller, right continuous and uniformly stochastic continuous on a neighborhood of the origin, then {yt} is Feller. 相似文献
4.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(5):559-564
Let (Bt)t≥0 be a standard Brownian motion starting at y, Xt = x+ ∫0tBs, ds, x ∈ (a, b). Let us set Tab = inf{t > 0 : Xt ∉ (a,b)}. In this paper, we compute the moments of the random variable BTa,b, and deduce the probability law of BTa,b. We show how to obtain the expectation E(x,y)(TabmBTabn). We also explicitly determine the probabilities P(x,y){XTab = a} and P(x,y) { XTab = b}. 相似文献
5.
《Insurance: Mathematics and Economics》1986,5(4):315-334
In actuarial sciences recently a lot of results have been derived for solving the problem sup {E(X−t) +:r.υ. X >0,EX′ = μ, for i = 1, 2, …, k}, x where μ, i = 1 to k as well as t are given. The present contribution solves this problem up to k = 4 analytically. 相似文献
6.
Yi Ci Zhang 《Stochastic Processes and their Applications》1983,14(2):175-186
In this paper we discuss the limit of the martingale e-αtKt as t→∞, where Xt is a continuous state branching process and E[Xt] = eαt. The important case is α > 0. Necessary and sufficient conditions are given for the limit to be positive. 相似文献
7.
Zhengdong Wang 《中国科学A辑(英文版)》1997,40(10):1022-1026
A Brownian motion {x t } t?0 on a compact Riemannian manifold M with a drift vector field X can be lifted to a diffusion process $\left\{ {\tilde x_t } \right\}_{t \ge 0} $ on M × Tk corresponding to an ?k valued smooth differential one-form A on M. The circulations (rotation numbers) of the lifted process $\left\{ {\tilde x_t } \right\}_{t \ge 0} $ around the k circles of Tk are studied. By choosing a certain ?k -valued differential one-form A, these circulations give the hidden circulation of {x t } t?0 in M and the rotation numbers of {x t } t?0 around some closed curves in M which generalize the first homology group H1(M,?) of M. 相似文献
8.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(6):515-520
We are interested in the approximation of the law of a multidimensional diffusion killed as it leaves an open set D, when the diffusion is approximated by its discrete Euler scheme, with discretization step N−1 T. We show that the error on Ex[1T< τ ƒ(XT)] (where τ = inft > 0: Xt ∉ D) is of order N−1/2, under some conditions on ƒ near the boundary of D. This rate is intrinsic to the problem of discrete killing time. 相似文献
9.
A.N Al-Hussaini 《Journal of Mathematical Analysis and Applications》1977,58(3):637-646
Let {Xt} be a continuous square integrable martingale. Denote its increasing (natural) process by {At}. Let St, Tt be the left and right inverses of At, respectively. Then for any square integrable martingale {Yt} defined on {Xt}, Yt = ∝0tψsdXs, R0 < t < S∞ where S∞ = limt→∞St, R0 = inf {t: Xt ≠ 0} provided that Y(T(t)) is σ(X(T(s)): s ? t)-measurable. All martingales are assumed to be zero at t = 0. Brownian motion and Poisson processes are considered also. 相似文献
10.
Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(sup_(t∈[0,T])X(t) x) is considered, as x →∞. 相似文献
11.
Robert Chen 《Journal of multivariate analysis》1978,8(2):328-333
Let {Xn}n≥1 be a sequence of independent and identically distributed random variables. For each integer n ≥ 1 and positive constants r, t, and ?, let Sn = Σj=1nXj and . In this paper, we prove that (1) lim?→0+?α(r?1)E{N∞(r, t, ?)} = K(r, t) if E(X1) = 0, Var(X1) = 1, and E(| X1 |t) < ∞, where 2 ≤ t < 2r ≤ 2t, , and ; (2) if 2 < t < 4, E(X1) = 0, Var(X1) > 0, and E(|X1|t) < ∞, where G(t, ?) = E{N∞(t, t, ?)} = Σn=1∞nt?2P{| Sn | > ?n} → ∞ as ? → 0+ and , i.e., H(t, ?) goes to infinity much faster than G(t, ?) as ? → 0+ if 2 < t < 4, E(X1) = 0, Var(X1) > 0, and E(| X1 |t) < ∞. Our results provide us with a much better and deeper understanding of the tail probability of a distribution. 相似文献
12.
Y. -K. Choi 《Acta Mathematica Hungarica》2009,123(4):331-355
This paper establishes the general moduli of continuity for l
∞-valued Gaussian random fields {X(t):= (X
1(t),X
2(t), h.), t ∈ [0, ∞)
N
} indexed by the N-dimensional parameter t:= (t
1,…,t
N
), under the explicit condition yielding that the covariance function of distinct increments of X
k
(t) for fixed k ≧ 1 is positive or nonpositive.
Supported by KOSEF-R01-2008-000-11418-0. 相似文献
13.
Stephen Portnoy 《Journal of multivariate analysis》1982,12(2):256-269
Let (T1, x1), (T2, x2), …, (Tn, xn) be a sample from a multivariate normal distribution where Ti are (unobservable) random variables and xi are random vectors in Rk. If the sample is either independent and identically distributed or satisfies a multivariate components of variance model, then the probability of correctly ordering {Ti} is maximized by ranking according to the order of the best linear predictors {E(Ti|xi)}. Furthermore, it orderings are chosen according to linear functions {b′xi} then the conditional probability of correct order given (Ti = t1; i = 1, …, n) is maximized when b′xi is the best linear predictor. Examples are given to show that linear predictors may not be optimal and that using a linear combination other that the best linear predictor may give a greater probability of correctly ordering {Ti} if {(Ti, xi)} are independent but not identically distributed, or if the distributions are not normal. 相似文献
14.
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
15.
Shuyuan He 《Journal of multivariate analysis》1996,58(2):182-188
We consider a stationary time series {Xt} given byXt=∑∞k=−∞ ψkZt−k, where {Zt} is a strictly stationary martingale difference white noise. Under assumptions that the spectral densityf(λ) of {Xt} is squared integrable andmτ ∑|k|?m ψ2k→0 for someτ>1/2, the asymptotic normality of the sample autocorrelations is shown. For a stationary long memoryARIMA(p, d, q) sequence, the conditionmτ ∑|k|?m ψ2k→0 for someτ>1/2 is equivalent to the squared integrability off(λ). This result extends Theorem 4.2 of Cavazos-Cadena [5], which were derived under the conditionm ∑|k|?m ψ2k→0. 相似文献
16.
Michael A. Kouritzin 《Journal of Theoretical Probability》1996,9(4):811-840
Since the novel work of Berkes and Philipp(3) much effort has been focused on establishing almost sure invariance principles of the form (1) $$\left| {\sum\limits_{i = 1}^{|\_t\_|} {x_1 - X_t } } \right| \ll t^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2} - \gamma } $$ where {x i ,i=1,2,3,...} is a sequence of random vectors and {X t ,t>-0} is a Brownian motion. In this note, we show that if {A k ,k=1,2,3,...} and {b k ,k=1,2,3,...} are processes satisfying almost-sure bounds analogous to Eq. (1), (where {X t ,t≥0} could be a more general Gauss-Markov process) then {h k ,k=1,2,3...}, the solution of the stochastic approximation or adaptive filtering algorithm (2) $$h_{k + 1} = h_k + \frac{1}{k}(b_k - A_k h_k )for{\text{ }}k{\text{ = 1,2,3}}...$$ also satisfies and almost sure invariance principle of the same type. 相似文献
17.
Let X be a symmetric Banach function space on [0, 1] and let E be a symmetric (quasi)-Banach sequence space. Let f = {f k } k=1 n , n ≥ 1 be an arbitrary sequence of independent random variables in X and let {e k } k=1 ∞ ? E be the standard unit vector sequence in E. This paper presents a deterministic characterization of the quantity in terms of the sum of disjoint copies of individual terms of f. We acknowledge key contributions by previous authors in detail in the introduction, however our approach is based on the important recent advances in the study of the Kruglov property of symmetric spaces made earlier by the authors. Authors acknowledge support from the ARC.
相似文献
$||||\sum\limits_{k = 1}^n {{f_k}{e_k}|{|_E}|{|_X}} $
18.
L. Kh. Poritskaya 《Mathematical Notes》1978,23(4):317-324
For a symmetric space E (Ref. Zh. Mat. IIB391) of measurable functions in the interval [0, 1] we introduce a characteristic $$\Pi \left( E \right) = \inf \left\| {\sum\nolimits_{i = 1}^n {x_i \left( {\frac{{t - \tau _{i - 1} }}{{\tau _i - \tau _{i - 1} }}} \right)\kappa \left[ {\tau _{i - 1} , \tau _i } \right]^{\left( t \right)} } } \right\|$$ where κ[τ i?1, τ i ](t) is a characteristic function and the inf is taken over all n and the setsx i ∈E, ∥x i ∥ E =1 and τ i ∈[0,1] (0=τ0<τ1<...<τ n =1,i=1, 2, ...,n). We prove the following. 相似文献
19.
Let k ? k′ be a field extension. We give relations between the kernels of higher derivations on k[X] and k′[X], where k[X]:= k[x 1,…, x n ] denotes the polynomial ring in n variables over the field k. More precisely, let D = {D n } n=0 ∞ a higher k-derivation on k[X] and D′ = {D′ n } n=0 ∞ a higher k′-derivation on k′[X] such that D′ m (x i ) = D m (x i ) for all m ? 0 and i = 1, 2,…, n. Then (1) k[X] D = k if and only if k′[X] D′ = k′; (2) k[X] D is a finitely generated k-algebra if and only if k′[X] D′ is a finitely generated k′-algebra. Furthermore, we also show that the kernel k[X] D of a higher derivation D of k[X] can be generated by a set of closed polynomials. 相似文献
20.
пУсть {f k; f k * ?X×X* — пОлНАь БИОРтОгОНАльНАь сИс тЕМА В БАНАхОВОМ пРОстРАН стВЕ X (X* — сОпРьжЕННОЕ пРОст РАНстВО). пУсть (?→+0) $$\begin{gathered} S_n f = \sum\limits_{k = 0}^n {f_k^* (f)f_k ,} K(f,t) = \mathop {\inf }\limits_{g \in Z} (\left\| {f - g} \right\|_x + t\left| g \right|_z ), \hfill \\ X_0 = \{ f \in X:\mathop {\lim }\limits_{n \to \infty } \left\| {S_n f - f} \right\|_x = 0\} ,X_\omega = \{ f \in X:K(f,t) = 0(\omega (t))\} , \hfill \\ \end{gathered} $$ гДЕZ?X — НЕкОтОРОЕ пОД пРОстРАНстВО с пОлУН ОРМОИ ¦·¦ И Ω — МОДУль НЕпРЕРыВНО стИ УДОВлЕтВОРьУЩИИ Усл ОВИУ sup Ω(t)/t=∞. пОслЕДОВАтЕ льНОстьΤ={Τ k} кОМплЕксНых ЧИ сЕл НАжыВАЕтсь МНОжИтЕл ЕМ сИльНОИ схОДИМОст И ДльX Τ, жАпИсьΤ?М[X Τ,X Τ], ЕслИ Д ль кАжДОгО ЁлЕМЕНтАf?X Τ сУЩЕстВ УЕт тАкОИ ЁлЕМЕНтf τ?х0, ЧтОf k * (f τ)=Τkf k * (f) Дль ВсЕхk. ДОкА жАНО сРЕДИ ДРУгИх слЕДУУЩ ЕЕ УтВЕРжДЕНИЕ. тЕОРЕМА. пУсmь {fk; f k * } —Н ЕкОтОРыИ (с, 1)-БАжИс тАк ОИ, ЧтО ВыпОлНьУтсь НЕРАВЕН стВА тИпА НЕРАВЕНстВА ДжЕ ксОНА с пОРьДкОМ O(?n) u тИ пА НЕРАВЕНстВА БЕРНшmЕИ НА с пОРьДкОМ O(1/?n). ЕслИ пОслЕДОВАтЕл ьНОсть Τ кВАжИВыпУкл А И ОгРАНИЧЕНА, тО $$\tau \in M[X_{\omega ,} X_0 ] \Leftrightarrow \omega (\varphi _n )\tau _n \left\| {S_n } \right\|_{[X,X]} = o(1).$$ ЁтОт ОБЩИИ пОДхОД НЕМ ЕДлЕННО ДАЕт клАссИЧ ЕскИЕ РЕжУльтАты, ОтНОсьЩИ Есь к ОДНОМЕРНыМ тРИгОНОМЕтРИЧЕскИМ РьДАМ. НО тЕпЕРь ВОжМО жНы ДАльНЕИшИЕ пРИлОжЕН Иь, НАпРИМЕР, к РАжлОжЕНИьМ пО пОлИ НОМАМ лЕжАНДРА, лАгЕР РА ИлИ ЁРМИтА. 相似文献