Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSpine decompositions and limit theorems for a class of critical superprocesses
201
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper, we first establish a decomposition theorem for size-biased Poisson random measures. As consequences of this decomposition theorem, we get a spine decomposition theorem and a 2-spine decomposition theorem for some critical superprocesses. Then we use these spine decomposition theorems to give probabilistic proofs of the asymptotic behavior of the survival probability and Yagloms exponential limit law for critical superprocesses.
rate research
Read More
We consider a critical superprocess ${X;mathbf P_mu}$ with general spatial motion and spatially dependent stable branching mechanism with lowest stable index $gamma_0 > 1$. We first show that, under some conditions, $mathbf P_{mu}(|X_t| eq 0)$ converges to $0$ as $tto infty$ and is regularly varying with index $(gamma_0-1)^{-1}$. Then we show that, for a large class of non-negative testing functions $f$, the distribution of ${X_t(f);mathbf P_mu(cdot||X_t| eq 0)}$, after appropriate rescaling, converges weakly to a positive random variable $mathbf z^{(gamma_0-1)}$ with Laplace transform $E[e^{-umathbf z^{(gamma_0-1)}}]=1-(1+u^{-(gamma_0-1)})^{-1/(gamma_0-1)}.$
We independently assign a non-negative value, as a capacity for the quantity of flows per unit time, with a distribution F to each edge on the Z^d lattice. We consider the maximum flows through the edges of two disjoint sets, that is from a source to a sink, in a large cube. In this paper, we show that the ratio of the maximum flow and the size of source is asymptotic to a constant. This constant is denoted by the flow constant.
We consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number of extracted balls of a certain color given the past is assumed to be hypergeometric. We prove some central limit theorems in the sense of stable convergence and of almost sure conditional convergence, which are stronger than convergence in distribution. The proven results provide asymptotic confidence intervals for the limit proportion, whose distribution is generally unknown. Moreover, we also consider the case of more urns subjected to some random common factors.
In this article, we consider limit theorems for some weighted type random sums (or discrete rough integrals). We introduce a general transfer principle from limit theorems for unweighted sums to limit theorems for weighted sums via rough path techniques. As a by-product, we provide a natural explanation of the various new asymptotic behaviors in contrast with the classical unweighted random sum case. We apply our principle to derive some weighted type Breuer-Major theorems, which generalize previous results to random sums that do not have to be in a finite sum of chaos. In this context, a Breuer-Major type criterion in notion of Hermite rank is obtained. We also consider some applications to realized power variations and to Itos formulas in law. In the end, we study the asymptotic behavior of weighted quadratic variations for some multi-dimensional Gaussian processes.
We derive an Ito-formula for the Dawson-Watanabe superprocess, a well-known class of measure-valued processes, extending the classical Ito-formula with respect to two aspects. Firstly, we extend the state-space of the underlying process $(X(t))_{tin [0,T]}$ to an infinite-dimensional one - the space of finite measure. Secondly, we extend the formula to functions $F(t,X_t)$ depending on the entire paths $X_t=(X(swedge t))_{s in [0,T]}$ up to times $t$. This later extension is usually called functional Ito-formula. Finally we remark on the application to predictable representation for martingales associated with superprocesses.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
