共查询到20条相似文献,搜索用时 15 毫秒
1.
Christiane Takacs 《Journal of Theoretical Probability》2001,14(3):699-715
We consider a random walk on
in a stationary and ergodic random environment, whose states are called types of the vertices of
. We find conditions for which the speed of the random walk is positive. In the case of a Markov chain environment with finitely many states, we give an explicit formula for the speed and for the asymptotic proportion of time spent at vertices of a certain type. Using these results, we compare the speed of random walks on
in environments of varying randomness. 相似文献
2.
Suppose that
,
, and
are three discrete probability distributions related by the equation (E):
, where
denotes the k-fold convolution of
In this paper, we investigate the relation between the asymptotic behaviors of
and
. It turns out that, for wide classes of sequences
and
, relation (E) implies that
, where
is the mean of
. The main object of this paper is to discuss the rate of convergence in this result. In our main results, we obtain O-estimates and exact asymptotic estimates for the difference
. 相似文献
3.
Packing Measure and Dimension of Random Fractals 总被引:1,自引:0,他引:1
We consider random fractals generated by random recursive constructions. We prove that the box-counting and packing dimensions of these random fractals, K, equals , their almost sure Hausdorff dimension. We show that some almost deterministic conditions known to ensure that the Hausdorff measure satisfies
also imply that the packing measure satisfies 0<
. When these conditions are not satisfied, it is known
. Correspondingly, we show that in this case
, provided a random strong open set condition is satisfied. We also find gauge functions (t) so that the
-packing measure is finite. 相似文献
4.
We introduce the notions of a Gibbs measure with the corresponding potential with association
(where
is a subset of the set
) of a Markov random field with memory
and measure with association
. It is proved that these three notions are equivalent. 相似文献
5.
Let W
n be an n × n random symmetric sparse matrix with independent identically distributed entries such that the values 1 and 0 are taken with probabilities p/n and 1-p/n, respectively; here
is independent of n. We show that the limit of the expected spectral distribution functions of W
n has a discrete part. Moreover, the set of positive probability points is dense in (- +). In particular, the points
, and 0 belong to this set. 相似文献
6.
Let
be a random walk with independent identically distributed increments
. We study the ratios of the probabilities P(S
n
>x) / P(1 > x) for all n and x. For some subclasses of subexponential distributions we find upper estimates uniform in x for the ratios which improve the available estimates for the whole class of subexponential distributions. We give some conditions sufficient for the asymptotic equivalence P(S
> x) E P(1 > x) as x . Here is a positive integer-valued random variable independent of
. The estimates obtained are also used to find the asymptotics of the tail distribution of the maximum of a random walk modulated by a regenerative process. 相似文献
7.
A nuclear space of distributions on Wiener space
was constructed by Gorostiza and Nualart [10] as a framework for studying weak convergence of trajectorial fluctuations of particle systems. A basic problem in recovering the usual time-evolution results from the trajectorial ones consists in associating in a unique way an
-valued process to a random distribution on
by localizing it at each time t
[0,1]. In this paper we solve this problem for a large class of random distributions which includes trajectorial fluctuation limits of some systems of diffusions. 相似文献
8.
Maher Mili 《Journal of Theoretical Probability》2000,13(3):717-731
Let K be respectively the parabolic biangle and the triangle in
and
be a sequence in [0, +[ such that limp (p)=+. According to Koornwinder and Schwartz,(7) for each
there exist a convolution structure (*(p)) such that (K, *(p)) is a commutative hypergroup. Consider now a random walk
on (K, *(p)), assume that this random walk is stopped after j(p) steps. Then under certain conditions given below we prove that the random variables
on K admit a selective limit theorems. The proofs depend on limit relations between the characters of these hypergroups and Laguerre polynomials that we give in this work. 相似文献
9.
If
is an RUC-basis in somecouple of non-commutative L
p-spaces, then
is an RUC-basic sequence in any non-commutative Orlicz or Lorentz space which is an interpolation space for this couple. 相似文献
10.
N. Guillotin-Plantard 《Journal of Theoretical Probability》2001,14(1):241-260
In this paper, we study a
d
-random walk
on nearest neighbours with transition probabilities generated by a dynamical system
. We prove, at first, that under some hypotheses,
verifies a local limit theorem. Then, we study these walks in a random scenery
, a sequence of independent, identically distributed and centred random variables and show that for certain dynamic random walks,
satisfies a strong law of large numbers. 相似文献
11.
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
12.
Paul H. Schuette 《Journal of Theoretical Probability》1994,7(1):3-45
Given a sequence of independent, but not necessarily identically distributed random variables,Y
i
, letS
k
denote thekth partial sum. Define a function
by taking
to be the piecewise linear interpolant of the points (k, S
k
), evaluated att, whereS
0=0, andk=0, 1, 2,... Fort[0, 1], let
. The
are called trajectories. With regularity and moment conditions on theY
i
, a large deviation principle is proved for the
. 相似文献
13.
It is shown that every probability measure on the interval [0, 1] gives rise
to a unique infinite random graph g on vertices
{v1,
v2, . . .}
and a sequence of random graphs gn on vertices
{v1, . . . ,
vn}
such that
.
In particular,
for Bernoulli graphs with
stable property Q,
can be strengthened to: probability space (, F, P),
set of infinite graphs
G(Q) ,
F with property Q such
that
.AMS Subject Classification: 05C80, 05C62. 相似文献
14.
Kameswarrao S. Casukhela 《Journal of Theoretical Probability》1997,10(3):759-771
An infinite sequence of random variables X=(X
1, X
2,...) is said to be spreadable if all subsequences of X have the same distribution. Ryll-Nardzewski showed that X is spreadable iff it is exchangeable. This result has been generalized to various discrete parameter and higher dimensional settings. In this paper we show that a random measure on the tetrahedral space
is spreadable, iff it can be extended to an exchangeable random measure on
. The result is a continuous parameter version of a theorem by Kallenberg. 相似文献
15.
We prove a local limit theorem for large deviations of the sums
, where
, is a Markov Gaussian random field,
is a bounded vector-valued function, and
. This paper generalizes the paper [13]. 相似文献
16.
We demonstrate how a well studied combinatorial optimizationproblem may be used as a new cryptographic primitive. The problemin question is that of finding a "large" clique in a randomgraph. While the largest clique in a random graph with nvertices and edge probability p is very likely tobe of size about
, it is widely conjecturedthat no polynomial-time algorithm exists which finds a cliqueof size
with significantprobability for any constant > 0. We presenta very simple method of exploiting this conjecture by hidinglarge cliques in random graphs. In particular, we show that ifthe conjecture is true, then when a large clique—of size,say,
is randomlyinserted (hidden) in a random graph, finding a clique ofsize
remains hard.Our analysis also covers the case of high edge probabilitieswhich allows us to insert cliques of size up to
. Our result suggests several cryptographicapplications, such as a simple one-way function. 相似文献
17.
Gerold Alsmeyer 《Journal of Theoretical Probability》2002,15(2):259-283
It is proved that for each random walk (S
n
)
n0 on
d
there exists a smallest measurable subgroup
of
d
, called minimal subgroup of (S
n
)
n0, such that P(S
n
)=1 for all n1.
can be defined as the set of all x
d
for which the difference of the time averages n
–1
n
k=1
P(S
k
) and n
–1
n
k=1
P(S
k
+x) converges to 0 in total variation norm as n. The related subgroup
* consisting of all x
d
for which lim
n P(S
n
)–P(S
n
+x)=0 is also considered and shown to be the minimal subgroup of the symmetrization of (S
n
)
n0. In the final section we consider quasi-invariance and admissible shifts of probability measures on
d
. The main result shows that, up to regular linear transformations, the only subgroups of
d
admitting a quasi-invariant measure are those of the form
1×...×
k
×
l–k
×{0}
d–l
, 0kld, with
1,...,
k
being countable subgroups of
. The proof is based on a result recently proved by Kharazishvili(3) which states no uncountable proper subgroup of
admits a quasi-invariant measure. 相似文献
18.
We consider random walks with small fixed steps inside of edges of a graph
, prescribing a natural rule of probabilities of jumps over a vertex. We show that after an appropriate rescaling such random walks weakly converge to the natural Brownian motion on
constructed in Ref. 1. 相似文献
19.
Let {S
n}
n0 be a random walk on the line. We give criteria for the existence of a nonrandom sequence n
i for which
respectively
We thereby obtain conditions for to be a strong limit point of {S
n} or {S
n
/n}. The first of these properties is shown to be equivalent to
for some sequence a
i , where T(a) is the exit time from the interval [–a,a]. We also obtain a general equivalence between
and
for an increasing function fand suitable sequences n
i and a
i. These sorts of properties are of interest in sequential analysis. Known conditions for
and
(divergence through the whole sequence n) are also simplified. 相似文献
20.
Gonzalo Perera 《Journal of Theoretical Probability》1997,10(3):581-603
We study the asymptotic distribution of
where A is a subset of
, A
N
= A[–N, N]
d
, v(A) = lim
N
card(A
N) (2N+1)
–d
(0, 1) and X is a stationary weakly dependent random field. We show that the geometry of A has a relevant influence on the problem. More specifically, S
N(A, X) is asymptotically normal for each X that satisfies certain mixting hypotheses if and only if
has a limit F(n; A) as N for each
. We also study the class of sets A that satisfy this condition. 相似文献