共查询到20条相似文献,搜索用时 11 毫秒
1.
Asymptotic behavior of the local time at the origin of q-dimensional fractional Brownian motion is considered when the index approaches the critical value 1/q. It is proved that, under a suitable (temporally inhomogeneous) normalization, it converges in law to the inverse of an extremal process which appears in the extreme value theory. 相似文献
2.
Let B
H
and
be two independent, d-dimensional fractional Brownian motions with Hurst parameter H∈(0,1). Assume d≥2. We prove that the intersection local time of B
H
and
exists in L
2 if and only if Hd<2.
相似文献
3.
Yiming JIANG 《数学年刊B辑(英文版)》2007,28(3):311-320
In this paper, the existence and smoothness of the collision local time are proved for two independent fractional Brownian motions, through L2 convergence and Chaos expansion. Furthermore, the regularity of the collision local time process is studied. 相似文献
4.
We give a result of stability in law of the local time of the fractional Brownian motion with respect to small perturbations
of the Hurst parameter. Concretely, we prove that the law (in the space of continuous functions) of the local time of the
fractional Brownian motion with Hurst parameter H converges weakly to that of the local time of , when H tends to H
0.
相似文献
5.
Vladimir I. Piterbarg 《Extremes》2001,4(2):147-164
We study probabilities of large extremes of the storage process Y(t) = sup
t
(X() - X(t) - c( - t)), where X(t) is the fractional Brownian motion. We derive asymptotic behavior of the maximum tail distribution for the process on fixed or slowly increased intervals by a reduction the problem to a large extremes problem for a Gaussian field. 相似文献
6.
本文利用白噪声分析的方法,讨论了分式布朗运动的局部时,即将其看作一个Hida分布.进一步,给出分式布朗运动的局部时的混沌分解以及局部时平方可积性. 相似文献
7.
In this paper, we introduce the linear fractional self-attracting diffusion driven by a fractional Brownian motion with Hurst
index 1/2<H<1, which is analogous to the linear self-attracting diffusion. For 1-dimensional process we study its convergence and the
corresponding weighted local time. For 2-dimensional process, as a related problem, we show that the renormalized self-intersection
local time exists in L
2 if 1/2<H<3/4.
The Project-sponsored by NSFC (10571025) and the Key Project of Chinese Ministry of Education (No.106076). 相似文献
8.
Hideaki Uemura 《随机分析与应用》2013,31(1):136-168
Abstract We determine the weighted local time for the multidimensional fractional Brownian motion from the occupation time formula. We also discuss on the Itô and Tanaka formula for the multidimensional fractional Brownian motion. In these formulas the Skorohod integral is applicable if the Hurst parameter of fractional Brownian motion is greater than 1/2. If the Hurst parameter is less than 1/2, then we use the Skorohod type integral introduced by Nualart and Zakai for the stochastic integral and establish the Itô and Tanaka formulas. 相似文献
9.
For a random element X of a nuclear space of distributions on Wiener space C([0,1],R
d
), the localization problem consists in projecting X at each time t[0,1] in order to define an S(R
d
)-valued process X={X(t),t[0,1]}, called the time-localization of X. The convergence problem consists in deriving weak convergence of time-localization processes (in C([0,1],S(R
d
)) in this paper) from weak convergence of the corresponding random distributions on C([0,1],R
d
). Partial steps towards the solution of this problem were carried out in previous papers, the tightness having remained unsolved. In this paper we complete the solution of the convergence problem via an extension of the time-localization procedure. As an example, a fluctuation limit of a system of fractional Brownian motions yields a new class of S(R
d
)-valued Gaussian processes, the fractional Brownian density processes. 相似文献
10.
Fix two rectangles A, B in [0, 1]
N
. Then the size of the random set of double points of the N-parameter Brownian motion
in R
d
, i.e, the set of pairs (s, t), where sA, tB, and W
s=W
t, can be measured as usual by a self-intersection local time. If A=B, we show that the critical dimension below which self-intersection local time does not explode, is given by d=2N. If A B is a p-dimensional rectangle, it is 4N–2p (0pN). If A B = , it is infinite. In all cases, we derive the rate of explosion of canonical approximations of self-intersection local time for dimensions above the critical one, and determine its smoothness in terms of the canonical Dirichlet structure on Wiener space. 相似文献
11.
Michel Talagrand 《Journal of Theoretical Probability》1996,9(1):191-213
We characterize the lower classes of fractional Brownian motion by an integral test.Work partially supported by an NSF grant. Equipe d'Analyse, Tour 46, U.A. at C.N.R.S. no 754, Université Paris VI, 4 place Jussieu, 75230 Paris Cedex 05, and Department of Mathematics, 231 West 18th Avenue, Columbus, Ohio 43210. 相似文献
12.
设X^H={X^H(t),t∈R+}是一个取值于R^d参数为H的次分数布朗运动.本文给出了X^H在单参数情况下局部时的Holder条件和尾概率估计.同时,还给出了X^H在多参数情况下局部时的存在性及L^2表示. 相似文献
13.
We define and prove the existence of a fractional Brownian motion indexed by a collection of closed subsets of a measure space.
This process is a generalization of the set-indexed Brownian motion, when the condition of independance is relaxed. Relations
with the Lévy fractional Brownian motion and with the fractional Brownian sheet are studied. We prove stationarity of the
increments and a property of self-similarity with respect to the action of solid motions. Moreover, we show that there no
“really nice” set indexed fractional Brownian motion other than set-indexed Brownian motion. Finally, behavior of the set-indexed
fractional Brownian motion along increasing paths is analysed.
相似文献
14.
本文研究了以分数布朗运动为输入过程的存储过程上穿高水平u形成的点过程的渐近泊松特性,结果表明当分数布朗运动参数H∈(0,1/2),u→∞时,该点过程弱收敛到泊松过程. 相似文献
15.
16.
17.
In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, L2 convergence and Chaos expansion. 相似文献
18.
Abstract We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H > 1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration and the classical Itô stochastic calculus. The existence result is based on the Yamada–Watanabe theorem. 相似文献
19.
B. L. S. Prakasa Rao 《随机分析与应用》2013,31(6):1199-1212
Abstract We investigate the general problem of estimating the translation of a stochastic process governed by a stochastic differential equation driven by a fractional Brownian motion. The special case of the Ornstein-Uhlenbeck process is discussed in particular. 相似文献
20.
Dong Sheng WU Yi Min XIAO 《数学学报(英文版)》2007,23(4):613-622
Let B^α = {B^α(t),t E R^N} be an (N,d)-fractional Brownian motion with Hurst index α∈ (0, 1). By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension results for the images of B^α when N 〉 αd. Our results extend those of Kaufman for one-dimensional Brownian motion. 相似文献