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1.
具有较一般分支特征的超布朗运动轨道性质 总被引:1,自引:0,他引:1
郭军义 《数学年刊A辑(中文版)》1997,(6)
本文研究具有较一般分支特征的超布朗运动{X(t)}t0的轨道性质.首先给出了它的一个击中概率的表达式,其次找到了它的支集蔓延速度的估计式及证明了支撑过程的右连续性,从而验证了Dawson,D.A.等人的猜想 相似文献
2.
设X={Xt,Pu}是d维超布朗运动,具有分支率函数A与一般分支机制ψ.讨论A满足什么条件时可以保证Xt具有绝对连续状态.特别当ψ(s,z,z)=z.时,Dawson与Fkischmann[2]讨论了类似问题.本文对他们的讨论进行了改进,将他们的结果推广到了ψ一般的情形,并且简化了他们对A所加的条件. 相似文献
3.
任艳霞 《数学年刊A辑(中文版)》2002,(4)
设X={Xt,Pμ}是d维超布朗运动,具有分支率函数A与一般分支机制ψ.讨论A满足什么条件时可以保证Xt具有绝对连续状态.特别当ψ(s,x,z)=z2时,Dawson与Fleischmann[2]讨论了类似问题.本文对他们的讨论进行了改进,将他们的结果推广到了ψ一般的情形,并且简化了他们对A所加的条件. 相似文献
4.
本文研究具有一类较广泛分支特征的超布朗运动在临近灭绝时的行为,主要得到了在临近灭绝时它的支撑的直径几乎处处收敛到零 相似文献
5.
本文证明了在一般的初始测度下,Dawson所获得的临界超布朗运动的渐 近定理并不成立,对于一般分支特征的临界的超布朗运动以及一般寝始测度,本文获得了它的渐近行为的阶的两个估计。 相似文献
6.
超布朗运动的灭绝时的分布 总被引:1,自引:0,他引:1
李存行 《数学年刊A辑(中文版)》1995,(5)
本文研究了超布朗运动的局部灭绝时的概率分布,并且得到了一类发展方程的解的一个性质。 相似文献
7.
唐加山 《数学年刊A辑(中文版)》1997,(6)
支撑性是超过程,作为取测度值马氏过程,所特有的性质.本文通过对双曲空间(常截面曲率为-1的单连通完备黎曼流形)Hd上超布朗运动{Xt}t0的研究给出关于{Xt}t0支撑的一些结果,同时也对Hd上方程ΔMu-u2+=0解的一些性质进行了讨论. 相似文献
8.
对双曲空间上的超布朗运动进行了研究,证明了该过程的范围属于某集合的概率可以表示为一个奇异边值问题的解.在得到了这个解的一个极限结果以后,给出了上述概率的一个渐近行为.对于维数d≥2,还证明了从黎曼测度出发的超过程在任何内点非空的有界Borel子集上的占位时是无穷的结论. 相似文献
9.
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
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11.
YAN Guojun & LI Zhanbing Medical School Shantou University Shantou China Department of Mathematics Bejing Normal University Beijing China 《中国科学A辑(英文版)》2006,49(4):451-476
In this paper, we give a unified construction for superprocesses with dependent spatial motion constructed by Dawson, Li, Wang and superprocesses of stochastic flows constructed by Ma and Xiang. Furthermore, we also give some examples and rescaled limits of the new class of superprocesses. 相似文献
12.
Consider the one-dimensional catalytic super-Brownian motion X (called the reactant) in the catalytic medium
which is an autonomous classical super-Brownian motion. We characterize
both in terms of a martingale problem and (in dimension one) as solution of a certain stochastic partial differential equation.
The focus of this paper is for dimension one the analysis of the longtime behavior via a mass-time-space rescaling. When scaling
time by a factor of K, space is scaled by K
η and mass by K
−η. We show that for every parameter value η ≥ 0 the rescaled processes converge as K→ ∞ in path space. While the catalyst’s limiting process exhibits a phase transition at η = 1, the reactant’s limit is always the same degenerate
process.
相似文献
13.
The functional central limit theorems are proved for super-Brownian motion with immigration and their occupation time processes. For the lower dimensions, the limiting processes are Gaussian processes; For the critical dimension, the limiting processes consist of two ingredient processes of different types. Interestingly, for the higher dimensions, the limiting process for the occupation time process is of a new type. 相似文献
14.
唐加山 《数学年刊A辑(中文版)》2007,(1)
对双曲空间上的超布朗运动进行了研究,证明了该过程的范围属于某集合的概率可以表示为一个奇异边值问题的解.在得到了这个解的一个极限结果以后,给出了上述概率的一个渐近行为.对于维数d≥2,还证明了从黎曼测度出发的超过程在任何内点非空的有界Borel子集上的占位时是无穷的结论. 相似文献
15.
A Continuous Super-Brownian Motion in a Super-Brownian Medium 总被引:2,自引:0,他引:2
A continuous super-Brownian motion
is constructed in which branching occurs only in the presence of catalysts which evolve themselves as a continuous super-Brownian motion
. More precisely, the collision local time
(in the sense of Barlow et al.
(1)) of an underlying Brownian motion path W with the catalytic mass process
goerns the branching (in the sense of Dynkin's additive functional approach). In the one-dimensional case, a new type of limit behavior is encountered: The total mass process converges to a limit without loss of expectation mass (persistence) and with a nonzero limiting variance, whereas starting with a Lebesgue measure
, stochastic convergence to
occurs. 相似文献
16.
We prove that the sequence of finite reflecting branching Brownian motion forests defined by Burdzy and Le Gall ([1]) converges in probability to the “super-Brownian motion with reflecting historical paths.” This solves an open problem posed in [1], where only tightness was proved for the sequence of approximations. Several results on path behavior were proved in [1] for all subsequential limits–they obviously hold for the unique limit found in the present paper.Mathematics Subject Classification (2000): Primary 60H15, Secondary 35R60Supported in part by NSF Grant DMS-0071486, Israel Science Foundation Grants 12/98 and 116/01 - 10.0, and the U.S.-Israel Binational Science Foundation (grant No. 2000065). 相似文献
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18.
陈振龙 《数学物理学报(B辑英文版)》2007,27(1):77-91
Let W be a two-parameter, Rd-valued generalized Brownian sheet. The author obtains an explicit Bessel-Riesz capacity estimate for the images of a two-dimensional set under W. He also presents the connections between the Lebesgue measure of the image of W and Bessel-Riesz capacity. His conclusions also solve a problem proposed by J.-P.Kahane. 相似文献
19.
Martin Ondrejat 《Czechoslovak Mathematical Journal》2005,55(4):1003-1039
The paper deals with three issues. First we show a sufficient condition for a cylindrical local martingale to be a stochastic
integral with respect to a cylindrical Wiener process. Secondly, we state an infinite dimensional version of the martingale
problem of Stroock and Varadhan, and finally we apply the results to show that a weak existence plus uniqueness in law for
deterministic initial conditions for an abstract stochastic evolution equation in a Banach space implies the strong Markov
property. 相似文献
20.
We establish an invariance principle for the fractional Brownian sheet, starting from discrete random fields constructed from two-parameter strong martingales. This is an approximation in law of the fractional Brownian sheet in Skorohord space in the plane. 相似文献