排序方式: 共有46条查询结果,搜索用时 15 毫秒
1.
Let {W i (t), t ∈ ?+}, i = 1, 2, be two Wiener processes, and let W 3 = {W 3(t), t ∈ ? + 2 } be a two-parameter Brownian sheet, all three processes being mutually independent. We derive upper and lower bounds for the boundary noncrossing probability P f = P{W 1(t 1) + W 2(t 2) + W 3(t) + f(t) ≤ u(t), t ∈ ? + 2 }, where f, u : ? + 2 → ? are two general measurable functions. We further show that, for large trend functions γf > 0, asymptotically, as γ → ∞, P γf is equivalent to \( {P}_{\gamma}\underset{\bar{\mkern6mu}}{{}_f} \) , where \( \underset{\bar{\mkern6mu}}{f} \) is the projection of f onto some closed convex set of the reproducing kernel Hilbert space of the field W(t) = W 1(t 1) + W 2(t 2) + W 3(t). It turns out that our approach is also applicable for the additive Brownian pillow. 相似文献
2.
Tail asymptotics of supremum of certain Gaussian processes over threshold dependent random intervals
Let {X(t),t ≥ 0} be a centered Gaussian process and let γ be a non-negative constant. In this paper we study the asymptotics of \(\mathbb {P} \left \{\underset {t\in [0,\mathcal {T}/u^{\gamma }]}\sup X(t)>u\right \}\) as \(u\rightarrow \infty \) , with \(\mathcal {T}\) an independent of X non-negative random variable. As an application, we derive the asymptotics of finite-time ruin probability of time-changed fractional Brownian motion risk processes. 相似文献
3.
Let \(X(t), t\in \mathcal {T}\) be a centered Gaussian random field with variance function σ 2(?) that attains its maximum at the unique point \(t_{0}\in \mathcal {T}\), and let \(M(\mathcal {T})=\sup _{t\in \mathcal {T}} X(t)\). For \(\mathcal {T}\) a compact subset of ?, the current literature explains the asymptotic tail behaviour of \(M(\mathcal {T})\) under some regularity conditions including that 1 ? σ(t) has a polynomial decrease to 0 as t → t 0. In this contribution we consider more general case that 1 ? σ(t) is regularly varying at t 0. We extend our analysis to Gaussian random fields defined on some compact set \(\mathcal {T}\subset \mathbb {R}^{2}\), deriving the exact tail asymptotics of \(M(\mathcal {T})\) for the class of Gaussian random fields with variance and correlation functions being regularly varying at t 0. A crucial novel element is the analysis of families of Gaussian random fields that do not possess locally additive dependence structures, which leads to qualitatively new types of asymptotics. 相似文献
4.
Enkelejd Hashorva 《Stochastic Processes and their Applications》2018,128(9):2952-2978
The recent contribution (Dieker and Mikosch, 2015) obtained representations of max-stable stationary Brown–Resnick process with spectral process being Gaussian. With motivations from Dieker and Mikosch (2015) we derive for general , representations for via exponential tilting of . Our findings concern Dieker–Mikosch representations of max-stable processes, two-sided extensions of stationary max-stable processes, inf-argmax representation of max-stable distributions, and new formulas for generalised Pickands constants. Our applications include conditions for the stationarity of , a characterisation of Gaussian distributions and an alternative proof of Kabluchko’s characterisation of Gaussian processes with stationary increments. 相似文献
5.
Enkelejd Hashorva 《Statistics & probability letters》2010,80(13-14):1070-1078
The residual dependence index of bivariate Gaussian distributions is determined by the correlation coefficient. This tail index is of certain statistical importance when extremes and related rare events of bivariate samples with asymptotic independent components are being modeled. In this paper we calculate the partial residual dependence indices of a multivariate elliptical random vector assuming that the associated random radius has distribution function in the Gumbel max-domain of attraction. Furthermore, we discuss the estimation of these indices when the associated random radius possesses a Weibull-tail distribution. 相似文献
6.
The paper deals with random vectors in , possessing the stochastic representation , where R is a positive random radius independent of the random vector and is a non-singular matrix. If is uniformly distributed on the unit sphere of , then for any integer m<d we have the stochastic representations and , with W≥0, such that W2 is a beta distributed random variable with parameters m/2,(d−m)/2 and (U1,…,Um),(Um+1,…,Ud) are independent uniformly distributed on the unit spheres of and , respectively. Assuming a more general stochastic representation for in this paper we introduce the class of beta-independent random vectors. For this new class we derive several conditional limiting results assuming that R has a distribution function in the max-domain of attraction of a univariate extreme value distribution function. We provide two applications concerning the Kotz approximation of the conditional distributions and the tail asymptotic behaviour of beta-independent bivariate random vectors. 相似文献
7.
Enkelejd Hashorva 《Extremes》2009,12(3):239-263
Let (S
1,S
2) = (R cos(Θ), R sin(Θ)) be a bivariate random vector with associated random radius R which has distribution function F being further independent of the random angle Θ. In this paper we investigate the asymptotic behaviour of the conditional
survivor probability when u approaches the upper endpoint of F. On the density function of Θ we impose a certain local asymptotic behaviour at 0, whereas for F we require that it belongs to the Gumbel max-domain of attraction. The main result of this contribution is an asymptotic
expansion of , which is then utilised to construct two estimators for the conditional distribution function . Furthermore, we allow Θ to depend on u.
相似文献
8.
We prove that the componentwise maximum of an i.i.d. triangular array of chi-square random vectors converges in distribution, under appropriate assumptions on the dependence within the vectors and after normalization, to the max-stable Hüsler–Reiss distribution. As a by-product we derive a conditional limit result. 相似文献
9.
Enkelejd Hashorva 《Extremes》2012,15(1):109-128
Let (X, Y) = (RU
1, RU
2) be a given bivariate scale mixture random vector, with R > 0 independent of the bivariate random vector (U
1, U
2). In this paper we derive exact asymptotic expansions of the joint survivor probability of (X, Y) assuming that R has distribution function in the Gumbel max-domain of attraction, and (U
1, U
2) has a specific local asymptotic behaviour around some absorbing point. We apply our results to investigate the asymptotic
behaviour of joint conditional excess distribution and the asymptotic independence for two models of bivariate scale mixture
distributions. 相似文献
10.
Let
be a triangular array of independent bivariate elliptical random vectors with the same distribution function as
where
is a bivariate spherical random vector. Under assumptions on the speed of convergence of
we show in this paper that the maxima of this triangular array is in the max-domain of attraction of a new max-id. distribution
function
, provided that
has distribution function in the max-domain of attraction of the Weibull distribution function
.
AMS 2000 Subject Classification Primary—60G70, 60F05 相似文献