共查询到20条相似文献,搜索用时 33 毫秒
1.
Wenming Hong 《Journal of Theoretical Probability》2003,16(4):899-922
Local large deviation principles are established in dimensions d3 for the super Brownian motion with random immigration X
t
, where the immigration rate is governed by the trajectory of another super-Brownian motion . The speed function is t for d4 and t
1/2 for d=3, compared with the existing results, the interesting phenomenon happened in d=4 with speed t (although only the upper large deviation bound is derived here) is just because the structure of this new model: the random immigration smooth the critical dimension in some sense. The rate function are characterized by an evolution equation. 相似文献
2.
Mei Zhang 《中国科学A辑(英文版)》2009,52(9):1875-1886
We prove fluctuation limit theorems for the occupation times of super-Brownian motion with immigration. The weak convergence of the processes is established, which improves the results in references. The limiting processes are Gaussian processes. 相似文献
3.
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
4.
本文给出了超布朗运动的质量过程在不灭绝条件下的极限分布的拉普拉斯变换的具体形式,并得出了在较一般的分支特征下使其值空间从MF(Rd)扩张到MP(Rd)的一个充分条件. 相似文献
5.
A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the
finite dimensional distribution sense. For the intermediate dimensions α < d < 2α (0 < α ≤ 2), the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2α and higher dimensions d < 2α, the limiting process is Brownian motion.
Zhang Mei, Functional central limit theorem for the super-brownian motion with super-Brownian immigration, J. Theoret. Probab.,
to appear. 相似文献
6.
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
7.
8.
Summary Almost sure convergence theorems are proved for Cesaro averages of continous functions in the case of the symmetric exclsion
processes in dimension d≧3. For the occupation time of a single site the same result is proved in all dimensions.
Partially supported by CNPq 相似文献
9.
《Stochastic Processes and their Applications》2002,99(2):323-348
Bivariate occupation measure dimension is a new dimension for multidimensional random processes. This dimension is given by the asymptotic behavior of its bivariate occupation measure. Firstly, we compare this dimension with the Hausdorff dimension. Secondly, we study relations between these dimensions and the existence of local time or self-intersection local time of the process. Finally, we compute the local correlation dimension of multidimensional Gaussian and stable processes with local Hölder properties and show it has the same value that the Hausdorff dimension of its image have. By the way, we give a new a.s. convergence of the bivariate occupation measure of a multidimensional fractional Brownian or particular stable motion (and thus of a spatial Brownian or Lévy stable motion). 相似文献
10.
For the one-dimensional telegraph process, we obtain explicitly the distribution of the occupation time of the positive half-line. The long-term limiting distribution is then derived when the initial location of the process is in the range of subnormal or normal deviations from the origin; in the former case, the limit is given by the arcsine law. These limit theorems are also extended to the case of more general occupation-type functionals. 相似文献
11.
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
12.
In this short communication we study a fluid queue with a finite buffer. The performance measure we are interested in is the occupation time over a finite time period, i.e., the fraction of time the workload process is below some fixed target level. Using an alternating renewal sequence, we determine the double transform of the occupation time; the occupation time for the finite buffer M/G/1 queue with phase-type jumps follows as a limiting case. 相似文献
13.
The solutions of various problems in the theories of queuing processes, branching processes, random graphs and others require the determination of the distribution of the sojourn time (occupation time) for the Brownian excursion. However, no standard method is available to solve this problem. In this paper we approximate the Brownian excursion by a suitably chosen random walk process and determine the moments of the sojourn time explicitly. By using a limiting approach, we obtain the corresponding moments for the Brownian excursion. The moments uniquely determine the distribution, enabling us to derive an explicit formula. 相似文献
14.
In this paper, we consider a class of semilinear parabolic differential equation where nonlinear term has local bounded coefficients. Under some assumptions, we get the existence and uniqueness of solution. Terminate to the time variable, we obtain the so called generalized Emden-Fowler equation and the asymptotic behavior of positive radial solutions have been given in all dimensions. At the end of this paper, we give its application to critical branching Brownian motion (also called measure-valued branching processes). 相似文献
15.
A class of infinite dimensional Ornstein-Uhlenbeck processes that arise as solutions of stochastic partial differential equations with noise generated by measure-valued catalytic processes is investigated. It will be shown that the catalytic Ornstein-Uhlenbeck process with super-Brownian catalyst in one dimension arises as a high density fluctuation limit of a super-Brownian motion in a super-Brownian catalyst with immigration. The main tools include Laplace transformations of stochastic processes, analysis of a non-linear partial differential equation and techniques on continuity and regularity based on properties of the Sobolev spaces. 相似文献
16.
Yuqiang Li 《Statistics & probability letters》2011,81(11):1604-1611
In this paper, some limit processes of occupation time fluctuations of the branching particle systems with varied branching laws from site to site are obtained. The results show that the varied branching laws can not affect the limit processes and the scaling parameters in the case of large dimensions, but in the case of critical dimensions, under suitable assumptions, it changes the limit processes with simple and isotropic spatial structures to those with complicated and anisotropic spatial structures and gives log corrections in the scaling parameters. 相似文献
17.
HONG Wenming 《数学年刊B辑(英文版)》1999,20(4):447-454
61.IntroductionLetW=[w,,ll.,.,s,t2o,aER']denoteastandardBrownianmotioninRdwithsendgroup{Pt,t2o},C(R')denotetheBanachspaceofcontinuousboundedfunctionsonRdequlppedwiththesupnorm.rk.(a):=(1 Ial')-p/',aERd,Cr(R'):-{feC(R'),lf(x)l5CIof.(x)}withsomeconstantCj,Mv(R'):={pisffedonmeasureonRdandJ(1 lxlp)-'p(dx)d.(P,i):=ff(x)p(dx),AisLebesgUemeasure.GiventheordinaryMP-valuedsuper-Brownianmotiono:=[o,,fl1,Ps,#,t2s2O,pEMP]asthecatalyticmedium,Dawsona… 相似文献
18.
Mei Zhang 《Journal of Theoretical Probability》2011,24(1):294-306
Central limit theorems of the occupation time of a superprocess over a stochastic flow are proved. For the critical and higher
dimensions d≥4, the limits are Gaussian variables. For d=3, the limit is conditional Gaussian. When the stochastic flow disappears, the results degenerate to those for the ordinary
super-Brownian motion. 相似文献
19.
I. Iscoe 《Probability Theory and Related Fields》1986,71(1):85-116
Summary A weighted occupation time is defined for measure-valued processes and a representation for it is obtained for a class of measure-valued branching random motions on R
d. Considered as a process in its own right, the first and second order asymptotics are found as time t. Specifically the finiteness of the total weighted occupation time is determined as a function of the dimension d, and when infinite, a central limit type renormalization is considered, yielding Gaussian or asymmetric stable generalized random fields in the limit. In one Gaussian case the results are contrasted in high versus low dimensions.Research supported in part by Natural Sciences and Engineering Research Council of Canada 相似文献
20.
Jim Pitman 《Probability Theory and Related Fields》1996,106(3):299-329
Summary. Local time processes parameterized by a circle, defined by the occupation density up to time T of Brownian motion with constant drift on the circle, are studied for various random times T. While such processes are typically non-Markovian, their Laplace functionals are expressed by series formulae related to
similar formulae for the Markovian local time processes subject to the Ray–Knight theorems for BM on the line, and for squares
of Bessel processes and their bridges. For T the time that BM on the circle first returns to its starting point after a complete loop around the circle, the local time
process is cyclically stationary, with same two-dimensional distributions, but not the same three-dimensional distributions,
as the sum of squares of two i.i.d. cyclically stationary Gaussian processes. This local time process is the infinitely divisible
sum of a Poisson point process of local time processes derived from Brownian excursions. The corresponding intensity measure
on path space, and similar Lévy measures derived from squares of Bessel processes, are described in terms of a 4-dimensional
Bessel bridge by Williams’ decomposition of It?’s law of Brownian excursions.
Received: 28 June 1995 相似文献