共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove a large deviations principle for the number of intersections of two independent infinite-time ranges in dimension 5 and greater, improving upon the moment bounds of Khanin, Mazel, Shlosman, and Sinaï [9]. This settles, in the discrete setting, a conjecture of van den Berg, Bolthausen, and den Hollander [15], who analyzed this question for the Wiener sausage in the finite-time horizon. The proof builds on their result (which was adapted in the discrete setting by Phetpradap [12]), and combines it with a series of tools that were developed in recent works of the authors [2, 3, 5]. Moreover, we show that most of the intersection occurs in a single box where both walks realize an occupation density of order 1. © 2022 Wiley Periodicals, Inc. 相似文献
2.
Harri Nyrhinen 《Journal of Theoretical Probability》2009,22(1):1-17
Let {S
n
;n=1,2,…} be a random walk in R
d
and E(S
1)=(μ
1,…,μ
d
). Let a
j
>μ
j
for j=1,…,d and A=(a
1,∞)×⋅⋅⋅×(a
d
,∞). We are interested in the probability P(S
n
/n∈A) for large n in the case where the components of S
1 are heavy tailed. An objective is to associate an exact power with the aforementioned probability. We also derive sharper
asymptotic bounds for the probability and show that in essence, the occurrence of the event {S
n
/n∈A} is caused by large single increments of the components in a specific way.
相似文献
3.
Let X
1, X
2,... be a sequence of i.i.d. non-negative random variables with heavy tails. W e study logarithmic asymptotics for the distributions of the partial sums S
n
= X
1 + ··· + X
n
. Our main interest is in the crude estimates P(S
n
> n
x
) n
–x + 1 for appropriate values of x where is a specific parameter. The related conjecture proposed by Gantert (Stat. Probab. Lett. 49, 113–118) is investigated. 相似文献
4.
Siberian Mathematical Journal - 相似文献
5.
We prove large and moderate deviation estimates for products of i.i.d. r.v.'s taking values on simply connected nilpotent Lie groups as a consequence of large and moderate deviation results for stochastic processes which are solutions of O.D.E. with random coefficients. 相似文献
6.
We study quenched distributions on random walks in a random potential on integer lattices of arbitrary dimension and with an arbitrary finite set of admissible steps. The potential can be unbounded and can depend on a few steps of the walk. Directed, undirected, and stretched polymers, as well as random walk in random environment, are covered. The restriction needed is on the moment of the potential, in relation to the degree of mixing of the ergodic environment. We derive two variational formulas for the limiting quenched free energy and prove a process‐level quenched large deviation principle (LDP) for the empirical measure. As a corollary we obtain LDPs for types of random walks in random environments not covered by earlier results. © 2012 Wiley Periodicals, Inc. 相似文献
7.
Siberian Mathematical Journal - We obtain a rather simple characterization of semiexponential distributions. This allows us to relax substantially the conditions for the fulfillment of the... 相似文献
8.
Xia Chen 《Journal of Theoretical Probability》2006,19(3):721-739
We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup
and the liminf laws of the iterated logarithm.
We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup
and the liminf laws of the iterated logarithm. 相似文献
9.
本文在一个相对较弱的假设之下,得到了复合更新风险模型中重尾随机和的精确大偏差等价式,该结果对文[1]中的结果进行了改进。 相似文献
10.
We study the asymptotics of the probability that the sum of random vectors belongs to a relatively small cube in the range of large deviations. 相似文献
11.
Generalized random graphs are considered where the presence or absence of an edge depends on the weights of its nodes. Our main interest is to investigate large deviations for the number of edges per node in such a generalized random graph, where the node weights are deterministic under some regularity conditions, as well as chosen i.i.d. from a finite set with positive components. When the node weights are random variables, obstacles arise because the independence among edges no longer exists, our main tools are some results of large deviations for mixtures. After calculating, our results show that the corresponding rate functions for the deterministic case and the random case are very different. 相似文献
12.
13.
Wen-sheng Wang 《应用数学学报(英文版)》2007,23(3):495-500
In this paper, we study strong laws of large numbers for random walks in random sceneries. Some mild sufficient conditions for the validity of strong laws of large numbers are obtained. 相似文献
14.
We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and the laws of the holding times are randomly distributed over the integer lattice. Our main result is a quenched large deviation principle for the position of the random walk. The rate function is given by the Legendre transform of the so-called Lyapunov exponents for the Laplace transform of the first passage time. By using this representation, we derive some asymptotics of the rate function in some special cases. 相似文献
15.
This paper is a further investigation of large deviations for sums of random variables S_n=sum form i=1 to n X_i and S(t)=sum form i=1 to N(t) X_i,(t≥0), where {X_n,n≥1) are independent identically distribution and non-negative random variables, and {N(t),t≥0} is a counting process of non-negative integer-valued random variables, independent of {X_n,n≥1}. In this paper, under the suppose F∈G, which is a bigger heavy-tailed class than C, proved large deviation results for sums of random variables. 相似文献
16.
考虑了重尾分布的多险种复合二项风险模型,在索赔额分布服从一致变化尾时,得到了其总索赔过程和总索赔盈利过程的大偏差,推广了经典复合二项风险模型的结论. 相似文献
17.
We obtain precise large deviations for heavy-tailed random sums
, of independent random variables.
are nonnegative integer-valued random variables independent of r.v. (X
i
)i
N with distribution functions F
i. We assume that the average of right tails of distribution functions F
i is equivalent to some distribution function with regularly varying tail. An example with the Pareto law as the limit function is given. 相似文献
18.
Wensheng Wang 《Journal of Theoretical Probability》2017,30(1):64-84
Let \(\{X_i, i\ge 1\}\) be i.i.d. \(\mathbb {R}^d\)-valued random vectors attracted to operator semi-stable laws and write \(S_n=\sum _{i=1}^{n}X_i\). This paper investigates precise large deviations for both the partial sums \(S_n\) and the random sums \(S_{N(t)}\), where N(t) is a counting process independent of the sequence \(\{X_i, i\ge 1\}\). In particular, we show for all unit vectors \(\theta \) the asymptotics which holds uniformly for x-region \([\gamma _n, \infty )\), where \(\langle \cdot , \cdot \rangle \) is the standard inner product on \(\mathbb {R}^d\) and \(\{\gamma _n\}\) is some monotone sequence of positive numbers. As applications, the precise large deviations for random sums of real-valued random variables with regularly varying tails and \(\mathbb {R}^d\)-valued random vectors with weakly negatively associated occurrences are proposed. The obtained results improve some related classical ones.
相似文献
$$\begin{aligned} {\mathbb P}(|\langle S_n,\theta \rangle |>x)\sim n{\mathbb P}(|\langle X,\theta \rangle |>x) \end{aligned}$$
19.
We firstly discuss the topological properties of the space of upper semicontinuous functions, and then we obtain large deviation principles for random upper semicontinuous functions under various topologies. Finally, we prove moderate deviation principles for random sets and random upper semicontinuous functions. 相似文献
20.
For Y1, Y2,…i .i .d . with Y1~N(μ, 1) and Sn=(?)Yi, the large deviations are obtained for theprobabilities that(?) conditionally given (i) Sm=0, and (ii) Smi=ξ. Applied these results to the double change points model with some nuisance parameters, we developed the large deviation for the significance level of the likelihood ratio test. 相似文献