共查询到20条相似文献,搜索用时 31 毫秒
1.
Let X={X(s)}s∈S be an almost sure continuous stochastic process (S compact subset of Rd) in the domain of attraction of some max-stable process, with index function constant over S. We study the tail distribution of ∫SX(s)ds, which turns out to be of Generalized Pareto type with an extra ‘spatial’ parameter (the areal coefficient from Coles and Tawn (1996) [3]). Moreover, we discuss how to estimate the tail probability P(∫SX(s)ds>x) for some high value x, based on independent and identically distributed copies of X. In the course we also give an estimator for the areal coefficient. We prove consistency of the proposed estimators. Our methods are applied to the total rainfall in the North Holland area; i.e. X represents in this case the rainfall over the region for which we have observations, and its integral amounts to total rainfall.The paper has two main purposes: first to formalize and justify the results of Coles and Tawn (1996) [3]; further we treat the problem in a non-parametric way as opposed to their fully parametric methods. 相似文献
2.
Erika Hausenblas 《Journal of Computational and Applied Mathematics》2010,235(1):33-58
We investigate the accuracy of approximation of E[φ(u(t))], where {u(t):t∈[0,∞)} is the solution of the stochastic wave equation driven by the space-time white noise and φ is an R-valued function defined on the Hilbert space L2(R). The approximation is done by the leap-frog scheme. We show that, under certain conditions on φ, the approximation by the leap-frog scheme is of order two. 相似文献
3.
Let (t∈[0,1]) be the indefinite Skorohod integral on the canonical probability space (Ω,F,P), and let Lt(x) (t∈[0,1], x∈R) be its the generalized local time introduced by Tudor in [C.A. Tudor, Martingale-type stochastic calculus for anticipating integral processes, Bernoulli 10 (2004) 313-325]. We prove that the generalized local time, as function of x, has the same Besov regularity as the Brownian motion, as function of t, under some conditions imposed on the anticipating integrand u. 相似文献
4.
In this paper we discuss the asymptotic behaviour of random contractions X=RS, where R, with distribution function F, is a positive random variable independent of S∈(0,1). Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of X assuming that F is in the max-domain of attraction of an extreme value distribution and the distribution function of S satisfies a regular variation property. We apply our result to derive the asymptotics of the probability of ruin for a particular discrete-time risk model. Further we quantify in our asymptotic setting the effect of the random scaling on the Conditional Tail Expectations, risk aggregation, and derive the joint asymptotic distribution of linear combinations of random contractions. 相似文献
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6.
T.A. Burton 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(12):3873-3882
We consider a scalar integral equation where a∈L2[0,∞), while C(t,s) has a significant singularity, but is convex when t−s>0. We construct a Liapunov functional and show that g(t,x(t))−a(t)∈L2[0,∞) and that x(t)−a(t)→0 pointwise as t→∞. Small perturbations are also added to the kernel. In addition, we consider both infinite and finite delay problems. This paper offers a first step toward treating discontinuous kernels with Liapunov functionals. 相似文献
7.
Stefano M. Iacus Nakahiro Yoshida 《Stochastic Processes and their Applications》2012,122(3):1068-1092
We consider a multidimensional Itô process Y=(Yt)t∈[0,T] with some unknown drift coefficient process bt and volatility coefficient σ(Xt,θ) with covariate process X=(Xt)t∈[0,T], the function σ(x,θ) being known up to θ∈Θ. For this model, we consider a change point problem for the parameter θ in the volatility component. The change is supposed to occur at some point t∗∈(0,T). Given discrete time observations from the process (X,Y), we propose quasi-maximum likelihood estimation of the change point. We present the rate of convergence of the change point estimator and the limit theorems of the asymptotically mixed type. 相似文献
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10.
Simeon M. Berman 《Stochastic Processes and their Applications》1983,15(3):213-238
Let X(t) be the trigonometric polynomial Σkj=0aj(Utcosjt+Vjsinjt), –∞< t<∞, where the coefficients Ut and Vt are random variables and aj is real. Suppose that these random variables have a joint distribution which is invariant under all orthogonal transformations of R2k–2. Then X(t) is stationary but not necessarily Gaussian. Put Lt(u) = Lebesgue measure {s: 0?s?t, X(s) > u}, and M(t) = max{X(s): 0?s?t}. Limit theorems for Lt(u) and for u→∞ are obtained under the hypothesis that the distribution of the random norm (Σkj=0(U2j+V2j))1 2 belongs to the domain of attraction of the extreme value distribution exp{ e–2}. The results are also extended to the random Fourier series (k=∞). 相似文献
11.
Svatoslav Staněk 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):e153
The paper discusses the existence of positive and dead core solutions of the singular differential equation (?(u″))′=λf(t,u,u′,u″) satisfying the boundary conditions u(0)=A, u(T)=A, min{u(t):t∈[0,T]}=0. Here λ is a nonnegative parameter, A is a positive constant and the Carathéodory function f(t,x,y,z) is singular at the value 0 of its space variable y. 相似文献
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Albert Ferreiro-Castilla 《Statistics & probability letters》2011,81(9):1380-1391
Let {X1(t)}0≤t≤1 and {X2(t)}0≤t≤1 be two independent continuous centered Gaussian processes with covariance functions R1 and R2. We show that if the covariance functions are of finite p-variation and q-variation respectively and such that p−1+q−1>1, then the Lévy area can be defined as a double Wiener-Itô integral with respect to an isonormal Gaussian process induced by X1 and X2. Moreover, some properties of the characteristic function of that generalised Lévy area are studied. 相似文献
14.
Elói Medina Galego 《Journal of Mathematical Analysis and Applications》2008,338(1):653-661
We first introduce the notion of (p,q,r)-complemented subspaces in Banach spaces, where p,q,r∈N. Then, given a couple of triples {(p,q,r),(s,t,u)} in N and putting Λ=(q+r−p)(t+u−s)−ru, we prove partially the following conjecture: For every pair of Banach spaces X and Y such that X is (p,q,r)-complemented in Y and Y is (s,t,u)-complemented in X, we have that X is isomorphic Y if and only if one of the following conditions holds:
- (a)
- Λ≠0, Λ divides p−q and s−t, p=1 or q=1 or s=1 or t=1.
- (b)
- p=q=s=t=1 and gcd(r,u)=1.
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Stephen James Wolfe 《Stochastic Processes and their Applications》1982,12(3):301-312
Let B1, B2, ... be a sequence of independent, identically distributed random variables, letX0 be a random variable that is independent ofBn forn?1, let ρ be a constant such that 0<ρ<1 and letX1,X2, ... be another sequence of random variables that are defined recursively by the relationshipsXn=ρXn-1+Bn. It can be shown that the sequence of random variablesX1,X2, ... converges in law to a random variableX if and only ifE[log+¦B1¦]<∞. In this paper we let {B(t):0≦t<∞} be a stochastic process with independent, homogeneous increments and define another stochastic process {X(t):0?t<∞} that stands in the same relationship to the stochastic process {B(t):0?t<∞} as the sequence of random variablesX1,X2,...stands toB1,B2,.... It is shown thatX(t) converges in law to a random variableX ast →+∞ if and only ifE[log+¦B(1)¦]<∞ in which caseX has a distribution function of class L. Several other related results are obtained. The main analytical tool used to obtain these results is a theorem of Lukacs concerning characteristic functions of certain stochastic integrals. 相似文献
17.
Ralph deLaubenfels 《Journal of Mathematical Analysis and Applications》2009,351(1):400-407
We characterize functions u from the real line into a Hilbert space that are the orbits of a unitary group {U(t)}t∈R; that is, u(t)=U(t)u(0), for all real t. One of the characterizations is that u be the Fourier transform of a certain type of vector-valued measure Z; we then use our characterizations to construct Z from u. 相似文献
18.
In this paper, we establish sharp two-sided estimates for the Green functions of relativistic stable processes (i.e. Green functions for non-local operators m−(m2/α−Δ)α/2) in half-space-like C1,1 open sets. The estimates are uniform in m∈(0,M] for each fixed M∈(0,∞). When m↓0, our estimates reduce to the sharp Green function estimates for −(−Δ)α/2 in such kind of open sets that were obtained recently in Chen and Tokle [12]. As a tool for proving our Green function estimates, we show that a boundary Harnack principle for Xm, which is uniform for all m∈(0,∞), holds for a large class of non-smooth open sets. 相似文献
19.
A. Amini-Harandi 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):132-2174
Suppose (X,d) be a complete metric space, and suppose F:X→CB(X) be a set-valued map satisfies H(Fx,Fy)≤ψ(d(x,y)), , where ψ:[0,∞)→[0,∞) is upper semicontinuous, ψ(t)<t for each t>0 and satisfies lim inft→∞(t−ψ(t))>0. Then F has a unique endpoint if and only if F has the approximate endpoint property. 相似文献
20.
Summary Consider the stationary sequenceX
1=G(Z
1),X
2=G(Z
2),..., whereG(·) is an arbitrary Borel function andZ
1,Z
2,... is a mean-zero stationary Gaussian sequence with covariance functionr(k)=E(Z
1
Z
k+1) satisfyingr(0)=1 and
k=1
|r(k)|
m
< , where, withI{·} denoting the indicator function andF(·) the continuous marginal distribution function of the sequence {X
n
}, the integerm is the Hermite rank of the family {I{G(·) x} –F(x):xR}. LetF
n
(·) be the empirical distribution function ofX
1,...,X
n
. We prove that, asn, the empirical processn
1/2{F
n
(·)-F(·)} converges in distribution to a Gaussian process in the spaceD[–,].Partially supported by NSF Grant DMS-9208067 相似文献