اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدStrong Law of Large Numbers for branching diffusions
152
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $X$ be the branching particle diffusion corresponding to the operator $Lu+beta (u^{2}-u)$ on $Dsubseteq mathbb{R}^{d}$ (where $beta geq 0$ and $beta otequiv 0$). Let $lambda_{c}$ denote the generalized principal eigenvalue for the operator $L+beta $ on $D$ and assume that it is finite. When $lambda_{c}>0$ and $L+beta-lambda_{c}$ satisfies certain spectral theoretical conditions, we prove that the random measure $exp {-lambda_{c}t}X_{t}$ converges almost surely in the vague topology as $t$ tends to infinity. This result is motivated by a cluster of articles due to Asmussen and Hering dating from the mid-seventies as well as the more recent work concerning analogous results for superdiffusions of cite{ET,EW}. We extend significantly the results in cite{AH76,AH77} and include some key examples of the branching process literature. As far as the proofs are concerned, we appeal to modern techniques concerning martingales and `spine decompositions or `immortal particle pictures.
قيم البحث
اقرأ أيضاً
We consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the lower and the upper Choquet integrals of the random v
ariables, provided either the random variables or the capacity are continuous.
We prove a strong law of large numbers for the Newtonian capacity of a Wiener sausage in the critical dimension four.
This work considers a many-server queueing system in which customers with i.i.d., generally distributed service times enter service in the order of arrival. The dynamics of the system is represented in terms of a process that describes the total numb
er of customers in the system, as well as a measure-valued process that keeps track of the ages of customers in service. Under mild assumptions on the service time distribution, as the number of servers goes to infinity, a law of large numbers (or fluid) limit is established for this pair of processes. The limit is characterised as the unique solution to a coupled pair of integral equations, which admits a fairly explicit representation. As a corollary, the fluid limits of several other functionals of interest, such as the waiting time, are also obtained. Furthermore, in the time-homogeneous setting, the fluid limit is shown to converge to its equilibrium. Along the way, some results of independent interest are obtained, including a continuous mapping result and a maximality property of the fluid limit. A motivation for studying these systems is that they arise as models of computer data systems and call centers.
For $1 le p < infty$, the Frechet $p$-mean of a probability distribution $mu$ on a metric space $(X,d)$ is the set $F_p(mu) := {arg,min}_{xin X}int_{X}d^p(x,y), dmu(y)$, which is taken to be empty if no minimizer exists. Given a sequence $(Y_i)_{i in
mathbb{N}}$ of independent, identically distributed random samples from some probability measure $mu$ on $X$, the Frechet $p$-means of the empirical measures, $F_p(frac{1}{n}sum_{i=1}^{n}delta_{Y_i})$ form a sequence of random closed subsets of $X$. We investigate the senses in which this sequence of random closed sets and related objects converge almost surely as $n to infty$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
