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1.
A. A. Borovkov 《Siberian Mathematical Journal》2005,46(1):35-55
Let
= _i = 1^n _i , S_n = _k n S_k
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共查询到20条相似文献,搜索用时 16 毫秒
1.
A. A. Borovkov 《Siberian Mathematical Journal》2005,46(1):35-55
Let
= _i = 1^n _i , S_n = _k n S_k |
#xa;
S_n = \sum\nolimits_{i = 1}^n \xi _i ,\bar S_n = \max _{k \leqslant n} S_k
. Assuming that some regularly varying functions majorize and minorize
$
F = \frac{1}{n}\sum\nolimits_{i = 1}^n {F_i }
$
F = \frac{1}{n}\sum\nolimits_{i = 1}^n {F_i }
, we find upper and lower bounds for the probabilities P(Sn > x) and P(
$
{\bar S_n }
$
{\bar S_n }
> x). These bounds are precise enough to yield asymptotics. We also study the asymptotics of the probability that a trajectory {Sk} crosses the remote boundary {g(k)}; i.e., the asymptotics of P(maxk$
\overset{\lower0.5em\hbox{$
\overset{\lower0.5em\hbox{
Matematicheski
$
\overset{\lower0.5em\hbox{$
\overset{\lower0.5em\hbox{
Zhurnal, Vol. 46, No. 1, pp. 46–70, January–February, 2005. 相似文献
2.
Summary We consider a system of independent random walks on . Let
n
(x) be the number of particles atx at timen, and letL
n
(x)=0(x)+ ... +
n
(x) be the total occupation time ofx by timen. In this paper we study the large deviations ofL
n
(0)–L
n
(1). The behavior we find is much different from that ofL
n
(0). We investigate the limiting behavior when the initial configurations has asymptotic density 1 and when 0(x) are i.i.d Poisson mean 1, finding that the asymptotics are different in these two cases.This work was done while the first author was on sabbatical at Cornell University. Both authors were partially supported by the National Science Foundation and the Army Research Office through the Mathematical Sciences Institute at Cornell 相似文献
3.
4.
Summary We prove large deviation theorems for occupation time functionals of independent random walks started from a Poisson field on Z
d. In dimensions 1 and 2 the large deviation tails are larger than exponential. Exact asymptotics are derived.Partially supported by the National Science Foundation under Grant MCS 81-02131 and MCS 81-00256Alfred P. Sloan Research Fellow 相似文献
5.
We establish large deviation principles and phase transition results for both quenched and annealed settings of nearest-neighbor random walks with constant drift in random nonnegative potentials on Zd. We complement the analysis of M.P.W. Zerner [Directional decay of the Green’s function for a random nonnegative potential on Zd, Ann. Appl. Probab. 8 (1996) 246–280], where a shape theorem on the Lyapunov functions and a large deviation principle in absence of the drift are achieved for the quenched setting. 相似文献
6.
7.
Let ξ, ξ1, ξ2, ... be independent identically distributed random variables, and S
n
:=Σ
j=1
n
,ξ
j
, $
\bar S
$
\bar S
:= sup
n≥0
S
n
. If Eξ = −a < 0 then we call transient those phenomena that happen to the distribution $
\bar S
$
\bar S
as a → 0 and $
\bar S
$
\bar S
tends to infinity in probability. We consider the case when Eξ fails to exist and study transient phenomena as a → 0 for the following two random walk models:
8.
9.
Large deviations for random walks in a mixing random environment and other (non‐Markov) random walks
F. Rassoul‐Agha 《纯数学与应用数学通讯》2004,57(9):1178-1196
We extend a recent work by S. R. S. Varadhan [8] on large deviations for random walks in a product random environment to include more general random walks on the lattice. In particular, some reinforced random walks and several classes of random walks in Gibbs fields are included. © 2004 Wiley Periodicals, Inc. 相似文献
10.
A. A. Borovkov 《Siberian Mathematical Journal》2011,52(3):402-410
We establish the local and so-called “extended” large deviation principles (see [1, 2]) for random walks whose jumps fail
to satisfy Cramér’s condition but have distributions varying regularly at infinity. 相似文献
11.
Summary Let
1 and
2 be Borel probability measures on
d
with finite moment generating functions. The main theorem in this paper proves the large deviation principle for a random walk whose transition mechanism is governed by
1 when the walk is in the left halfspace 1 = {x
d
:x
10} and whose transition mechanism is governed by
2 when the walk is in the right halfspace 2 = {x
d
:x
1>0}. When the measures
1 and
2 are equal, the main theorem reduces to Cramér's Theorem.This research was supported in part by a grant from the National Science Foundation (NSF-DMS-8902333)This research was supported in part by a grant from the National Science Foundation (NSF-DMS-8901138) and in part by a Lady Davis Fellowship while visiting the Faculty of Industrial Engineering and Management at the Technion during the spring semester of 1989 相似文献
12.
In this paper, we consider a family of Markov bridges with jumps constructed from truncated stable processes. These Markov bridges depend on a small parameter ?>0, and have fixed initial and terminal positions. We propose a new method to prove a large deviation principle for this family of bridges based on compact level sets, change of measures, duality and various global and local estimates of transition densities for truncated stable processes. 相似文献
13.
A. A. Mogul’skii 《Siberian Mathematical Journal》2006,47(6):1084-1101
Suppose that ξ, ξ(1), ξ(2), ... are independent identically distributed random variables such that ?ξ is semiexponential; i.e., $P( - \xi \geqslant t) = e^{ - t^\beta L(t)} $ is a slowly varying function as t → ∞ possessing some smoothness properties. Let E ξ = 0, D ξ = 1, and S(k) = ξ(1) + ? + ξ(k). Given d > 0, define the first upcrossing time η +(u) = inf{k ≥ 1: S(k) + kd > u} at nonnegative level u ≥ 0 of the walk S(k) + kd with positive drift d > 0. We prove that, under general conditions, the following relation is valid for $u = (n) \in \left[ {0, dn - N_n \sqrt n } \right]$ :
14.
Amir Dembo Nina Gantert Yuval Peres Ofer Zeitouni 《Probability Theory and Related Fields》2002,122(2):241-288
In the study of large deviations for random walks in random environment, a key distinction has emerged between quenched asymptotics, conditional on the environment, and annealed asymptotics, obtained from averaging over environments. In this paper we consider a simple random walk {X
n
} on a Galton–Watson tree T, i.e., on the family tree arising from a supercritical branching process. Denote by |X
n
| the distance between the node X
n
and the root of T. Our main result is the almost sure equality of the large deviation rate function for |X
n
|/n under the “quenched measure” (conditional upon T), and the rate function for the same ratio under the “annealed measure” (averaging on T according to the Galton–Watson distribution). This equality hinges on a concentration of measure phenomenon for the momentum of the walk. (The momentum at level n, for a specific tree T, is the average, over random walk paths, of the forward drift at the hitting point of that level). This concentration, or
certainty, is a consequence of the uncertainty in the location of the hitting point. We also obtain similar results when {X
n
} is a λ-biased walk on a Galton–Watson tree, even though in that case there is no known formula for the asymptotic speed.
Our arguments rely at several points on a “ubiquity” lemma for Galton–Watson trees, due to Grimmett and Kesten (1984).
Received: 15 November 2000 / Revised version: 27 February 2001 / Published online: 19 December 2001 相似文献
15.
The deviation functional (or integral) describes the logarithmic asymptotics of the probabilities of large deviations of trajectories of the random walks generated by the sums of random variables (vectors) (see [1, 2] for instance). In this article we define it on a broader function space than previously and under weaker assumptions on the distributions of jumps of the random walk. The deviation integral turns out the Darboux integral ∫ F(t, u) of a semiadditive interval function F(t, u) of a particular form. We study the properties of the deviation integral and use the results elsewhere in [3] to prove some generalizations of the large deviation principle established previously under rather restrictive assumptions. 相似文献
16.
17.
Let S 0 = 0, {S n , n ≥ 1} be a random walk generated by a sequence of i.i.d. random variables X 1, X 2, . . . and let $\tau ^{-}={\rm min} \{ n \geq 1:S_{n}\leq 0 \}$ and $\tau ^{+}={\rm min}\{n\geq1:S_{n} > 0\} $ . Assuming that the distribution of X 1 belongs to the domain of attraction of an α-stable law we study the asymptotic behavior, as ${n\rightarrow \infty }$ , of the local probabilities ${\bf P}{(\tau ^{\pm }=n)}$ and prove the Gnedenko and Stone type conditional local limit theorems for the probabilities ${\bf P}{(S_{n} \in [x,x+\Delta )|\tau^{-} > n)}$ with fixed Δ and ${x=x(n)\in (0,\infty )}$ . 相似文献
18.
Stefano Olla 《Probability Theory and Related Fields》1988,77(3):343-357
A large deviation principle for Gibbs random fields on Zd is proven and a corresponding large deviations proof of the Gibbs variational formula is given. A generalization of the Lanford theory of large deviations is also obtained.This work was partially supported by NSF-DMR81-14726 相似文献
19.
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