共查询到17条相似文献,搜索用时 46 毫秒
1.
布朗运动是一种重要的随机过程,它的首出时的分布在很多方面有着重要的应用.该文讨论了布朗运动关于任意曲线边界的首出时的问题,求出了布朗运动停在双侧(单侧)曲线边界内的概率的分析表达式. 相似文献
2.
3.
4.
利用Dirichlet外问题与漂移布朗运动之间存在的密切联系,对Dirichlet外问题提出了一种新的有效的概率数值方法,这种方法运用了解的随机表达式、布朗运动、漂移布朗运动以及球面首中位置和时间的分布等. 相似文献
5.
针对定解区域是无界区域的Dirichlet外问题,提出了一种新的有效的概率数值方法,它是从解的随机表达式出发,将无界区域上的问题转化成区域边界上的问题.此时,只要在边界上进行剖分,将问题离散化,然后在无界区域外的有界区域内构作一个辅助球,并且利用布朗运动、漂移布朗运动从球外一点出发,首中球面的位置和时间的分布等,就可以获得Dirichlet外问题的数值解. 相似文献
6.
7.
应用Le Gall的超布朗运动的轨道构造,研究超布朗运动关于区域的着中方式,证明了它在首中一个区域时,其支撑集与区域闭包的交集的点数不大于2,并提出了一个猜想。 相似文献
8.
非线性飘移布朗运动的极值分布 总被引:1,自引:0,他引:1
本文研究了从x出发的非线性漂移布朗运动的极大值、极小值和首达时问题.利用测度变换以及布朗运动的一些重要性质,如反射原理,增量的独立性等,获得了两种极值分布函数的精确表达式,得到了首达时的分布函数.结果表明,线性漂移布朗运动的极大值极小值以及首达时的分布问题的有关结果是本文结论的推论,最后给出一个例子. 相似文献
10.
11.
In this paper, we
discuss the problem of extreme value for Brownian motion with positive drift. We obtain
the joint distribution of the maximum excursion and the minimum excursion. 相似文献
12.
L Yu-hua~ 《数学季刊》2007,22(1):57-62
In this paper,we discuss the problem of extreme value for Brownian motion with positive drift.We obtain the joint distribution of the maximum excursion and the minimum excursion. 相似文献
13.
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
14.
We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed
as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class includes many interesting
processes in real applications, e.g., Ornstein–Uhlenbeck, growth processes and geometric Brownian motion with time dependent
drift. This method applies to both one-sided and two-sided general nonlinear boundaries, which may be discontinuous. Using
this approach explicit formulas for boundary crossing probabilities for certain nonlinear boundaries are obtained, which are
useful in evaluation and comparison of various computational algorithms. Moreover, numerical computation can be easily done
by Monte Carlo integration and the approximation errors for general boundaries are automatically calculated. Some numerical
examples are presented.
相似文献
15.
With appropriate regularity assumptions on the increasing concave function x=(t)<0, the hitting time density p(t) for a transient curve x=(t) by a 1-dimensional Brownian motion is shown to satisfy
Here r is the probability of eventually hitting the curve and (t)=t
–1/2(t). 相似文献
16.
Bischoff Wolfgang Miller Frank Hashorva Enkelejd Hüsler Jürg 《Methodology and Computing in Applied Probability》2003,5(3):271-287
Let us consider a signal-plus-noise model h(z)+B
0(z), z [0,1], where > 0, h: [0,1] , and B
0 is a Brownian bridge. We establish the asymptotics for the boundary crossing probability of the weighted signal-plus-noise model for , that is P (sup
z [0,1]
w(z)( h(z)+B
0(z))>c), for , (1) where w: [0,1] [0, is a weight function and c>0 is arbitrary. By the large deviation principle one gets a result with a constant which is the solution of a minimizing problem. In this paper we show an asymptotic expansion that is stronger than large deviation. As byproduct of our result we obtain the solution of the minimizing problem occurring in the large deviation expression. It is worth mentioning that the probability considered in (1) appears as power of the weighted Kolmogorov test applied to the test problem H
0: h 0 against the alternative K: h>0 in the signal-plus-noise model. 相似文献
17.
Iterated Brownian Motion in Parabola-Shaped Domains 总被引:1,自引:0,他引:1
Erkan Nane 《Potential Analysis》2006,24(2):105-123
Iterated Brownian motion Zt serves as a physical model for diffusions in a crack. If τD(Z) is the first exit time of this processes from a domain D⊂ℝn, started at z∈D, then Pz[τD(Z)>t] is the distribution of the lifetime of the process in D. In this paper we determine the large time asymptotics of
which gives exponential integrability of
for parabola-shaped domains of the form Pα={(x,Y)∈ℝ×ℝn−1:x>0, |Y|<Axα}, for 0<α<1, A>0. We also obtain similar results for twisted domains in ℝ2 as defined in DeBlassie and Smits: Brownian motion in twisted domains, Preprint, 2004. In particular, for a planar iterated
Brownian motion in a parabola
we find that for z∈℘
Mathematics Subject Classifications (2000) 60J65, 60K99.
Erkan Nane: Supported in part by NSF Grant # 9700585-DMS. 相似文献