共查询到20条相似文献,搜索用时 15 毫秒
1.
T. Sottinen 《Journal of Theoretical Probability》2004,17(2):309-325
We consider Gaussian processes that are equivalent in law to the fractional Brownian motion and their canonical representations. We prove a Hitsuda type representation theorem for the fractional Brownian motion with Hurst index H1/2. For the case H>1/2 we show that such a representation cannot hold. We also consider briefly the connection between Hitsuda and Girsanov representations. Using the Hitsuda representation we consider a certain special kind of Gaussian stochastic equation with fractional Brownian motion as noise. 相似文献
2.
Philippe Carmona Laure Coutin G. Montseny 《Statistical Inference for Stochastic Processes》2000,3(1-2):161-171
We study a class of processes which have a moving average representation with respect to a fixed driving martingale, and can be represented as a mixture of semi-martingale processes. When the driving martingale is Gaussian we obtain a numerically efficient approximation scheme and a central limit theorem (a typical process in this class is fractional Brownian motion). 相似文献
3.
Let XH = {XH(s),s ∈RN1} and X K = {XK(t),t ∈R N2} be two independent anisotropic Gaussian random fields with values in R d with indices H =(H1,...,HN1) ∈(0,1)N1,K =(K1,...,KN2) ∈(0,1) N2,respectively.Existence of intersections of the sample paths of X H and X K is studied.More generally,let E1■RN1,E2■RN2 and FRd be Borel sets.A necessary condition and a sufficient condition for P{(XH(E1)∩XK(E2))∩F≠Ф}>0 in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1×E2×F in the metric space(RN1+N2+d,) are proved,where is a metric defined in terms of H and K.These results are applicable to solutions of stochastic heat equations driven by space-time Gaussian noise and fractional Brownian sheets. 相似文献
4.
Zong-mao Cheng Xiu-yun Wang Zheng-yan Lin 《应用数学学报(英文版)》2006,22(1):81-90
In this paper, we introduce a class of Gaussian processes Y={Y(t):t∈R^N},the so called hifractional Brownian motion with the indcxes H=(H1,…,HN)and α. We consider the (N, d, H, α) Gaussian random field x(t) = (x1 (t),..., xd(t)),where X1 (t),…, Xd(t) are independent copies of Y(t), At first we show the existence and join continuity of the local times of X = {X(t), t ∈ R+^N}, then we consider the HSlder conditions for the local times. 相似文献
5.
Small Deviations for Some Multi-Parameter Gaussian Processes 总被引:1,自引:0,他引:1
We prove some general lower bounds for the probability that a multi-parameter Gaussian process has very small values. These results, when applied to a certain class of fractional Brownian sheets, yield the exact rate for their so-called small ball probability. We show by example how to use such results to compute the Hausdorff dimension of some exceptional sets determined by maximal increments. 相似文献
6.
7.
Wenbo V. Li 《Journal of Theoretical Probability》1999,12(4):971-984
Let {X(t); 0t1} be a real-valued continuous Gaussian Markov process with mean zero and covariance (s, t) = EX(s) X(t) 0 for 0<s, t<1. It is known that we can write (s, t) = G(min(s, t)) H(max(s, t)) with G>0, H>0 and G/H nondecreasing on the interval (0, 1). We show that
In the critical case, i.e. this integral is infinite, we provide the correct rate (up to a constant) for log P(sup0<t1 |X(t)|<) as 0 under regularity conditions. 相似文献
8.
9.
Jean-Francois Coeurjolly Emilio Porcu 《Journal of computational and graphical statistics》2018,27(2):278-290
This article is concerned with the study of the embedding circulant matrix method to simulate stationary complex-valued Gaussian sequences. The method is, in particular, shown to be well-suited to generate circularly symmetric stationary Gaussian processes. We provide simple conditions on the complex covariance function ensuring the theoretical validity of the minimal embedding circulant matrix method. We show that these conditions are satisfied by many examples and illustrate the simulation algorithm. In particular, we present a simulation study involving the circularly symmetric fractional Gaussian noise, a model introduced in this article. Supplementary material for this article is available online. 相似文献
10.
S. G. Kobel’kov 《Mathematical Notes》2006,80(3-4):372-379
For a family of real-valued Gaussian processes ξ u (t), t ∈ [0, T], we obtain an exact asymptotics of the probability of crossing a level u as u → ∞ under certain conditions on the variance and correlation. This result is applied to the investigation of excursions of a stationary zero-mean process above a barrier increasing to infinity. 相似文献
11.
The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-field Stochastic Differential Equations
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In this paper, some properties of a stochastic convolution driven by tempered fractional Brownian motion are obtained. Based on this result, we get the existence and uniqueness of stochastic mean-field equation driven by tempered fractional Brownian motion. Furthermore, combining with the Banach fixed point theorem and the properties of Mittag-Leffler functions, we study the existence and uniqueness of mild solution for a kind of time fractional mean-field stochastic differential equation driven by tempered fractional Brownian motion. 相似文献
12.
13.
Orey suggested the definition of an index for a Gaussian process with stationary increments which determines various properties of the sample paths of this process. We provide an extension of the definition of the Orey index towards a second-order stochastic process which may not have stationary increments and estimate the Orey index towards a Gaussian process from discrete observations of its sample paths. 相似文献
14.
15.
In this article we investigate the equivalence of underdetermined differential equations and differential equations with deviations
of second order with respect to the pseudogroup of transformations = φ(x), ȳ = ȳ() = L(x) + y(x), = () = M(x) + z(x). Our main aim is to determine such equations that admit a large pseudogroup of symmetries. Instead the common direct calculations,
we use some more advanced tools from differential geometry, however, our exposition is self-contained and only the most fundamental
properties of differential forms are employed.
This research has been conducted at the Department of Mathematics as part of the research project CEZ: Progressive reliable
and durable structures, MSM 0021630519. 相似文献
16.
TRUMAN Aubrey 《中国科学 数学(英文版)》2012,55(10):1971-1976
Using Girsanov transformation,we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type,in such a manner that the obtained BurgersKPZ equation characterizes the path-independence property of the density process of Girsanov transformation for the stochastic differential equation.Our assertion also holds for SDEs on a connected differential manifold. 相似文献
17.
FEI Wei-yin 《高校应用数学学报(英文版)》2014,29(1):53-66
This paper is concerned with a class of uncertain backward stochastic differential equations (UBSDEs) driven by both an m-dimensional Brownian motion and a d-dimensional canonical process with uniform Lipschitzian coefficients. Such equations can be useful in mod- elling hybrid systems, where the phenomena are simultaneously subjected to two kinds of un- certainties: randomness and uncertainty. The solutions of UBSDEs are the uncertain stochastic processes. Thus, the existence and uniqueness of solutions to UBSDEs with Lipschitzian coeffi- cients are proved. 相似文献
18.
V. Tryhuk 《Czechoslovak Mathematical Journal》2008,58(3):605-635
In this article, the equivalence and symmetries of underdetermined differential equations and differential equations with
deviations of the first order are considered with respect to the pseudogroup of transformations . That means, the transformed unknown function is obtained by means of the change of the independent variable and subsequent multiplication by a nonvanishing factor. Instead
of the common direct calculations, we use some more advanced tools from differential geometry; however, the exposition is
self-contained and only the most fundamental properties of differential forms are employed. We refer to analogous achievements
in literature. In particular, the generalized higher symmetry problem involving a finite number of invariants of the kind
is compared to similar results obtained by means of auxiliary functional equations. 相似文献
19.
本文将推广在[3]中由E.Csaki及M.Csorgo所引入的关于随机过程不等式,并把它应用到某些随机过程中,从而得到这些随机过程的一些极限定理. 相似文献
20.
Let
be a fractional Brownian motion with parameter 0 < H < 1. We are interested in the estimation of this parameter. To achieve this goal, we consider certain functionals of the
second order increments of b
H
(·), using variation technics. Based on an almost-sure convergence theorem for general functionals, we single out particular
functionals that allows to construct certain regression models for the parameter H. We show that this regression based estimator for H is asymptotically unbiased, consistent and that it satisfies a Central Limit Theorem.
相似文献