共查询到20条相似文献,搜索用时 62 毫秒
1.
We consider subordinators in the domain of attraction at 0 of a stable subordinator (where ); thus, with the property that , the tail function of the canonical measure of , is regularly varying of index as . We also analyse the boundary case, , when is slowly varying at 0. When , we show that converges in distribution, as , to the random variable . This latter random variable, as a function of , converges in distribution as to the inverse of an exponential random variable. We prove these convergences, also generalised to functional versions (convergence in ), and to trimmed versions, whereby a fixed number of its largest jumps up to a specified time are subtracted from the process. The case produces convergence to an extremal process constructed from ordered jumps of a Cauchy subordinator. Our results generalise random walk and stable process results of Darling, Cressie, Kasahara, Kotani and Watanabe. 相似文献
2.
Le Chen Yaozhong Hu David Nualart 《Stochastic Processes and their Applications》2019,129(12):5073-5112
This paper studies the nonlinear stochastic partial differential equation of fractional orders both in space and time variables: where is the space–time white noise, , , and . Fundamental solutions and their properties, in particular the nonnegativity, are derived. The existence and uniqueness of solution together with the moment bounds of the solution are obtained under Dalang’s condition: . In some cases, the initial data can be measures. When , we prove the sample path regularity of the solution. 相似文献
3.
Alexander Iksanov Konrad Kolesko Matthias Meiners 《Stochastic Processes and their Applications》2019,129(11):4480-4499
Let be Biggins’ martingale associated with a supercritical branching random walk, and let be its almost sure limit. Under a natural condition for the offspring point process in the branching random walk, we show that if the law of belongs to the domain of normal attraction of an -stable distribution for some , then, as , there is weak convergence of the tail process , properly normalized, to a random scale multiple of a stationary autoregressive process of order one with -stable marginals. 相似文献
4.
The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has requests to transmit and is idle, it tries to access the channel at a rate proportional to . A stochastic model of such an algorithm is investigated in the case of the star network, in which nodes can transmit simultaneously, but interfere with a central node 0 in such a way that node 0 cannot transmit while one of the other nodes does. One studies the impact of the log policy on these interacting communication nodes. A fluid scaling analysis of the network is derived with the scaling parameter being the norm of the initial state. It is shown that the asymptotic fluid behavior of the system is a consequence of the evolution of the state of the network on a specific time scale . The main result is that, on this time scale and under appropriate conditions, the state of a node with index is of the order of , with , where is a piecewise linear function. Convergence results on the fluid time scale and a stability property are derived as a consequence of this study. 相似文献
5.
Luca Avena Hakan Güldaş Remco van der Hofstad Frank den Hollander 《Stochastic Processes and their Applications》2019,129(9):3360-3375
We consider a dynamic random graph on vertices that is obtained by starting from a random graph generated according to the configuration model with a prescribed degree sequence and at each unit of time randomly rewiring a fraction of the edges. We are interested in the mixing time of a random walk without backtracking on this dynamic random graph in the limit as , when is chosen such that . In Avena et al. (2018) we found that, under mild regularity conditions on the degree sequence, the mixing time is of order when . In the present paper we investigate what happens when . It turns out that the mixing time is of order , with the scaled mixing time exhibiting a one-sided cutoff when and a two-sided cutoff when . The occurrence of a one-sided cutoff is a rare phenomenon. In our setting it comes from a competition between the time scales of mixing on the static graph, as identified by Ben-Hamou and Salez (2017), and the regeneration time of first stepping across a rewired edge. 相似文献
6.
7.
Balázs Gerencsér 《Stochastic Processes and their Applications》2019,129(9):3570-3584
The paper concerns a particular example of the Gibbs sampler and its mixing efficiency. Coordinates of a point are rerandomized in the unit square to approach a stationary distribution with density proportional to for with some large parameter .Diaconis conjectured the mixing time of this process to be which we confirm in this paper. This improves on the currently known estimate. 相似文献
8.
Yongsheng Song 《Stochastic Processes and their Applications》2019,129(6):2066-2085
As is known, if is a -Brownian motion, a process of form , , is a non-increasing -martingale. In this paper, we shall show that a non-increasing -martingale cannot be form of or , , which implies that the decomposition for generalized -Itô processes is unique: For arbitrary , and non-increasing -martingales , if then we have , and. As an application, we give a characterization to the -Sobolev spaces introduced in Peng and Song (2015). 相似文献
9.
Ion Grama Ronan Lauvergnat Émile Le Page 《Stochastic Processes and their Applications》2019,129(7):2485-2527
Let be a branching process in a random environment defined by a Markov chain with values in a finite state space . Let be the probability law generated by the trajectories of starting at We study the asymptotic behaviour of the joint survival probability , as in the critical and strongly, intermediate and weakly subcritical cases. 相似文献
10.
We consider a -parameter Hermite process with Hurst index and we study its limit behavior in distribution when the Hurst parameters (or a part of them) converge to and/or 1. The limit obtained is Gaussian (when at least one parameter tends to ) and non-Gaussian (when at least one-parameter tends to 1 and none converges to ). 相似文献
11.
13.
14.
Zhouxin Li 《Journal of Differential Equations》2019,266(11):7264-7290
We prove the existence of positive solutions of the following singular quasilinear Schrödinger equations at critical growth via variational methods, where , , , , . It is interesting that we do not need to add a weight function to control . 相似文献
15.
In this paper, we study the existence and concentration behavior of minimizers for , here and where and are constants. By the Gagliardo–Nirenberg inequality, we get the sharp existence of global constraint minimizers of for when , and . For the case , we prove that the global constraint minimizers of behave like for some when c is large, where is, up to translations, the unique positive solution of in and , and . 相似文献
16.
I. Berkes 《Stochastic Processes and their Applications》2019,129(11):4500-4509
The St. Petersburg paradox (Bernoulli, 1738) concerns the fair entry fee in a game where the winnings are distributed as . The tails of are not regularly varying and the sequence of accumulated gains has, suitably centered and normalized, a class of semistable laws as subsequential limit distributions (Martin-Löf, 1985; Csörg? and Dodunekova, 1991). This has led to a clarification of the paradox and an interesting and unusual asymptotic theory in past decades. In this paper we prove that can be approximated by a semistable Lévy process with a.s. error and, surprisingly, the error term is asymptotically normal, exhibiting an unexpected central limit theorem in St. Petersburg theory. 相似文献
17.
《Discrete Mathematics》2019,342(4):1159-1169
In this article, we study symmetric designs admitting a flag-transitive and point-primitive automorphism group whose socle is . We prove that there exist eight non-isomorphic such designs for which and is either , or . 相似文献
18.
19.
20.
A matching in a 3-uniform hypergraph is a set of pairwise disjoint edges. We use to denote the 3-uniform hypergraph whose vertex set can be partitioned into two vertex classes and of size and , respectively, and whose edge set consists of all the triples containing at least two vertices of . Let be a 3-uniform hypergraph of order with no isolated vertex and for any two adjacent vertices . In this paper, we show that contains a matching of size if and only if is not a subgraph of . This result improves our previous one in Zhang and Lu (2018). 相似文献