THE OCCUPATION DENSITY FIELD FOR THE CATALYTIC SUPER-BROWNIAN MOTION

It is proved that the occupation time of the catalytic super-Brownian motion is absolutely continuous for d = 1, and the occupation density field is jointly continuous and jointly Holder continuous.

Moderate Deviation for the Single Point Catalytic Super-Brownian Motion

We establish the moderate deviation for the density process of the single point catalytic super-Brownian motion. The main tools are the abstract Gaertner-Ellis theorem, Dawson-Gaertner the- orem and the contraction principle. The rate function is expressed by the Fenchel-Legendre transform of log-exponential moment generation function.

ON THE WEIGHTED OCCUPATION TIME AND SUPPORT OF SUPER-BROWNIAN MOTION CONDITIONED ON NON-EXTINCTION

This paper investigates the property of super-Brownian motion conditioned on non-extinction. The authors obtain a representation of Laplace functional for the weighted occupation time of this class of processes. By this, they get a result about the distribution of the support of it.

SOME PATH PROPERTIES OF BROWNIAN MOTION AND SUPER-BROWNIAN MOTION ON THE SIERPINSKI GASKET

We study in this paper the path properties of the Brownian motion and super-Brownian motion on the fractal structure-the Sierpinski gasket. At first some results about the limiting behaviour of its increments are obtained and a kind of law of iterated logarithm is proved. Then A Lower bound of the spreading speed of its corresponding super-Brownian motion is obtained.

ON THE EMPTY BALLS OF A CRITICAL OR SUBCRITICAL BRANCHING RANDOM WALK

Let{Z_(n)}_(n)≥0 be a critical or subcritical d-dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure onℝ^(d).Denote by R_(n):=sup{u>0:Z_(n)({x∈ℝ^(d):∣x∣<u})=0}the radius of the largest empty ball centered at the origin of Zn.In this work,we prove that after suitable renormalization,Rn converges in law to some non-degenerate distribution as n→∈.Furthermore,our work shows that the renormalization scales depend on the offspring law and the dimension of the branching random walk.This completes the results of Révész[13]for the critical binary branching Wiener process.

Central limit theorem for the occupation time of catalyticsuper-Brownian motion

The catalytic super_Brownian motion has been considered. If both the catalytic medium process Q and CSBM started with Lebesgue measure λ, the central limit theorem for occupation time of CSBM has been obtained in dimension 3 for P-λ_a.s.Q.

Supercritical branching Brownian motion with catalytic branching at the origin

We consider a catalytic branching Brownian motion with general branching which takes place only when particles are at the origin at a rate β>0 on the local time scale. We first establish a spine decomposition for the case wherein the particles have a positive probability of having no children. Then using this tool, we obtain results regarding the asymptotic behavior of the number of particles above λt at time t for λ>0. Under an L log L condition, we prove a strong law of large numbers for this catalytic branching Brownian motion.

330MW机组SCR脱硝系统内飞灰运动的数值模拟分析

烟气中混杂着大量细小的飞灰颗粒,易造成SCR脱硝系统催化剂的堵塞和磨损。以某330MW燃煤电厂SCR烟气脱硝装置为原型,采用FLUENT软件对系统内烟气——飞灰颗粒气固两相流进行数值模拟,对不同工况下飞灰运动轨迹进行预测,判断飞灰颗粒的集中区域。模拟结果对工程实际中吹灰器的布置及选型、保证脱硝反应的高效进行提供了一定的理论支持。

An asymptotic result of super-Brownian motion on hyperbolic space

SUPERPROCESS is one kind of measure-valued branching Markov processes. In the recentdecades many results of superprocesses on Euclidean spaces and on general abstract spaces havebeen obtained, but there is only little work on Riemannian manifold. In this note, wewill consider the super-Brownian motions on the hyperbolic space of dimension d and give anasymptotic result of this process (see Corollary 1 below). Iscoe investigated a similar prob-

Moderate deviation for super-Brownian motion with immigration

We prove a moderate deviation principle for a super-Brownian motion with immigration of all dimensions, and consequently fill the gap between the central limit theorem and large deviation principle.

Immigration process in catalytic medium

The longtime behavior of the immigration process associated with a catalytic super-Brown-ian motion is studied. A large number law is proved in dimension d≤3 and a central limit theorem is proved for dimension d = 3.

Absolutely continuous states of exit measures for super-Brownian motions with branching restricted to a hyperplane

The exit measures of super-Brownian motions with branching mechanism $\psi (z) = z^\alpha ,1< \alpha \leqslant 2$ from a bounded smooth domain D in ?d+1 are known to be absolutely continuous with respect to the surface area on ?D if $d< \frac{2}{{a - 1}}$ whereas in the case $d > 1 + \frac{2}{{a - 1}}$ they are singular. However, if the branching is restricted to a singular hyperplane, it is proved that they have absolutely continuous states for alld≥1.

Local extinction of super-Brownian motion on Sierpinski gasket

The Brownian motion and super-Brownian motion on the Sierpinski gasket are studied. Firstly it is proved that the local extinction property is possessed by the super-Brownian motion on this fractal structure. This fact is also true even in the presence of catalyst. Secondly it is proved that the paths of the Brownian motion on the Sierpinski gasket are dense in some sense.

Finite time extinction of super-Brownian motions with deterministic catalyst

In this paper we consider a super-Brownian motion X with branching mechanism k(x)z α, where k(x) > 0 is a bounded H?lder continuous function on ?d and ${}_{{}_x \in \mathbb{R}^d }k(x) = 0$ . We prove that ifk(x)?‖x‖?l (0?l<∞) for sufficiently large x, then X has compact support property, and for dimension d = 1, ifk(x)?exp(=?l‖x‖)(0?l<∞) for sufficiently large x, then X also has compact support property. The maximal order of k(x) for finite time extinction is different between d = 1, d = 2 and d ≥ 3: it isO(‖x‖?(α+1)) in one dimension,O(‖x‖?2(log ‖x‖))?(α+1)) in two dimensions, andO(‖x‖2) in higher dimensions. These growth orders also turn out to be the maximum order for the nonexistence of a positive solution for 1/2Δu=k(x)u α.

The Behavior of Super-Brownian Motion near Extinction

We start from a super-Brownian motion with the branching mechanism presented by Dawson and Vinogradov. Its behaviour near extinction is studied in this paper, and the main result is that the diameter of the support tends to zero almost surely at the time of extinction.

ON POSITIVE SOLUTIONS OF ONE CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS

In this paper, we establish a 1-1 correspondence between positive solutionsof one class of nonlinear differential equations and a class of harmonic functions.These results give an explicit description of E.B.Dynkin's class Ha of positive harmonic functions.

S-polar sets of super-Brownian motions and solutions of nonlinear differential equations

This paper gives probabilistic expressions of theminimal and maximal positive solutions of the partial differential equation -1/2△v(x) + γ(x)v(x)α = 0 in D, where D is a regular domain in Rd(d ≥ 3) such that its complement Dc is compact, γ(x) is a positive bounded integrable function in D, and 1 ＜α≤ 2. As an application, some necessary and sufficient conditions for a compact set to be S-polar are presented.

Moderate deviations for the quenched mean of the super-Brownian motion with random immigration

Moderate deviations for the quenched mean of the super-Brownian motion with random immigration are proved for 3≤d≤6, which fills in the gap between central limit theorem(CLT)and large deviation principle(LDP).

Some scaled limit theorems for an immigration super-Brownian motion

In this paper,the small time limit behaviors for an immigration super-Brownian motion are studied,where the immigration is determined by Lebesgue measure.We first prove a functional central limit theorem,and then study the large and moderate deviations associated with this central tendency.

On the weak convergence of super-Brownian motion with immigration

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.