共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
T. Simon 《Journal of Theoretical Probability》2004,17(4):979-1002
Let Z
t
, t 0 be a strictly stable process on
with index (0, 2]. We prove that for every p > , there exists = , p
and
such that
where || Z||
p
stands for the strong p-variation of Z on [0,1]. The critical exponent p
, takes a different shape according as | Z| is a subordinator and p > 1, or not. The small ball constant
is explicitly computed when p > 1, and a lower bound on
is easily obtained in the general case. In the symmetric case and when p > 2, we can also give an upper bound on
in terms of the Brownian small ball constant under the (1/p)-Höder semi-norm. Along the way, we remark that the positive random variable
is not necessarily stable when p > 1, which gives a negative answer to an old question of P. E. Greenwood.10 相似文献
3.
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
4.
Let {S
n} be a random walk, generated by i.i.d. increments X
i which drifts weakly to in the sense that
as n . Suppose k0, k1, and E|X
1|1\k
= if k>1. Then we show that the probability that S. crosses the curve nan
K before it crosses the curve n –an
k tends to 1 as a . This intuitively plausible result is not true for k = 1, however, and for 1/2 <k<1, the converse results are not true in general, either. More general boundaries g(n) than g(n) = n
k are also considered, and we also prove similar results for first passages out of regions like { (n, y): n1, |y| (a + n)
k
} as a . 相似文献
5.
Emanuela Ughi 《Geometriae Dedicata》1988,26(3):241-245
A family of conics in PG(2,q) is called saturated if any line LPG(2,q) is incident with at least one conic of the family. Then, if <(q+1)/2, the support of is a (k,n)-blocking set. It is shown that in this way one can get blocking sets whose character n is small compared to q; it is also shown that cannot be taken independent of q, but must necessarily increase as q does. 相似文献
6.
Let
, the parameter space, be an open subset ofR
k
,k1. For each
, let the r.v.'sX
n
,n=1, 2,... be defined on the probability space (X, P
) and take values in (S,S,L) whereS is a Borel subset of a Euclidean space andL is the -field of Borel subsets ofS. ForhR
k
and a sequence of p.d. normalizing matrices
n
=
n
k × k
(0 set
n
*
= * = 0 +
n
h, where 0 is the true value of , such that *,
. Let
n
(*, *)( be the log-likelihood ratio of the probability measure
with respect to the probability measure
, whereP
n
is the restriction ofP
over
n
= (X
1,X
2,...,X
n
. In this paper we, under a very general dependence setup obtain a rate of convergence of the normalized log-likelihood ratio statistic to Standard Normal Variable. Two examples are taken into account. 相似文献
7.
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
8.
Rita Solomyak 《Journal of Theoretical Probability》1999,12(2):523-548
Let be a Cayley graph of a finitely generated group G. Subgraphs which contain all vertices of , have no cycles, and no finite connected components are called essential spanning forests. The set
of all such subgraphs can be endowed with a compact topology, and G acts on
by translations. We define a uniform G-invariant probability measure on
show that is mixing, and give a sufficient condition for directional tail triviality. For non-cocompact Fuchsian groups we show how can be computed on cylinder sets. We obtain as a corollary, that the tail -algebra is trivial, and that the rate of convergence to mixing is exponential. The transfer-current function (an analogue to the Green function), is computed explicitly for the Modular and Hecke groups. 相似文献
9.
Hans-Peter Scheffler 《Journal of Theoretical Probability》1994,7(4):767-792
LetG be a stratified Lie group and (t)t 0 be a continuous convolution semigroup of probability measures onG. A probability measurev is said to belong to the
-domain of attraction of 1, if there exists a sequence (a
n
) of positive real numbers such that
weakly, where 1 denotes the natural dilation onG. We prove convergence criteria for discrete convolution semigroups. These are used to obtain a simple necessary and sufficient condition for the existence of sucha
n
if (t)t 0 has no Gaussian component. For the proof we introduce the notion of regularly varying measures onG and develop the necessary theory of regular variation. 相似文献
10.
Let < SL
n
(
) be a subgroup of finite index, where n 5. Suppose acts continuously on a manifold M, where 1(M) =
n
, preserving a measure that is positive on open sets. Further assume that the induced action on H
1(M) is non-trivial. We show there exists a finite index subgroup < and a equivariant continuous map : M
n
that induces an isomorphism on fundamental group. We prove more general results providing continuous quotients in cases where 1(M) surjects onto a finitely generated torsion free nilpotent group. We also give some new examples of manifolds with actions. 相似文献
11.
Let X be a real-valued random variable and
a -algebra. We show that the minimum
-distance between X and a random variable distributed as X and independant of
can be viewed as a dependence coefficient (
,X) whose definition is comparable (but different) to that of the usual -mixing coefficient between
and (X). We compare this new coefficient to other well known measures of dependence, and we show that it can be easily computed in various situations, such as causal Bernoulli shifts or stable Markov chains defined via iterative random maps. Next, we use coupling techniques to obtain Bennett and Rosenthal-type inequalities for partial sums of -dependent sequences. The former is used to prove a strong invariance principle for partial sums. 相似文献
12.
A compound Poisson process is of the form
where Z, Z
1, Z
2, are arbitrary i.i.d. random variables and N
is an independent Poisson random variable with parameter . This paper identifies the degree of precision that can be achieved when using exponential bounds together with a single truncation to approximate
. The truncation level introduced depends only on and Z and not on the overall exceedance level a. 相似文献
13.
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
14.
Let (Z
n
)
n 0 be a supercritical Galton–Watson process with finite re-production mean and normalized limit W=lim
n –n
Z
n
. Let further : [0,) [0,) be a convex differentiable function with (0)=(0)=0 and such that (
) is convex with concave derivative for some n 0. By using convex function inequalities due to Topchii and Vatutin, and Burkholder, Davis and Gundy, we prove that 0 < E
(W) < if, and only if,
, where
We further show that functions (x)=x
L(x) which are regularly varying of order 1 at are covered by this result if {2
n
: n 0 } and under an additional condition also if =2
n
for some n0. This was obtained in a slightly weaker form and analytically by Bingham and Doney. If > 1, then
grows at the same order of magnitude as (x) so that
and E
(Z
1)< are equivalent. However, =1 implies
and hence that
is a strictly stronger condition than E
(Z
1) < . If (x)=x log
p
x for some p > 0 it can be shown that
grows like x log
p+1
x, as x. For this special case the result is due to Athreya. As a by-product we also provide a new proof of the Kesten–Stigum result that E
Z
1 log Z
1 < and EW > 0 are equivalent. 相似文献
15.
Let (X
t
) be a one dimensional diffusion corresponding to the operator
, starting from x>0 and T
0 be the hitting time of 0. Consider the family of positive solutions of the equation
with (0, ), where
. We show that the distribution of the h-process induced by any such is
, for a suitable sequence of stopping times (S
M
: M0) related to which converges to with M. We also give analytical conditions for
, where
is the smallest point of increase of the spectral measure associated to
. 相似文献
16.
Werner Varnhorn 《Acta Appl Math》1994,37(1-2):205-214
We construct strong solutionsu, p/of the general nonhomogeneous Stokes equations -u + p=f inG, ·u=g inG, u= on in an exterior domainG n (n3) with boundary of class C2. Our approach uses a localization technique: With the help of suitable cut-off functions and the solution of the divergence equation ·=g inG, = 0 on , the exterior domain problem is reduced to the entire space problem and an interior problem. 相似文献
17.
Pavel Pyrih 《Potential Analysis》1994,3(3):273-281
We study the set of functions in quasi-analytic classes and the set of finely holomorphic functions. We show that no one of these two sets is contained in the other.LetI denote the set of complex functionsf: for which there exists a quasi-analytic classC{M
n} containingf. Let denote the set of complex functionsf: for which there exist a fine domainU containing the real line and a function
finely holomorphic onU satisfyingf(x)=
(x) for allx . The power of unique continuation is incomparable in these two cases (I\ is non-empty, \I is non-empty).Research supported by the grant No. 201/93/2174 of Czech Grant Agency and by the grant No. 354 of Charles University. 相似文献
18.
For nilpotent quantum groups [as introduced by Franz et al.
(7)], we show that (in sharp contrast to the classical case) the symmetrization
of a probability distribution and the first moments of together determine uniquely the original distribution . 相似文献
19.
Michael Voit 《Journal of Theoretical Probability》1996,9(2):353-370
Let
be the field , , or of real dimension . For each dimensiond2, we study isotropic random walks(Y
1)10 on the projective space
with natural metricD where the random walk starts at some
with jumps at each step of a size depending ond. Then the random variablesX
1
d
:=cosD(Y
1
d
,x
0
d
) form a Markov chain on [–1, 1] whose transition probabilities are related to Jacobi convolutions on [–1, 1]. We prove that, ford, the random variables (vd/2)(X
l(d)
d
+1) tend in distribution to a noncentral
2-distribution where the noncentrality parameter depends on relations between the numbers of steps and the jump sizes. We also derive another limit theorem for
as well as thed-spheresS
d
ford. 相似文献
20.
Yimin Xiao 《Journal of Theoretical Probability》1997,10(4):849-866
Let X(t) (tR) be a real-valued centered Gaussian process with stationary increments. We assume that there exist positive constants
0, C
1, and c
2 such that for any tR and hR with |h|0
and for any 0r<min{|t|, 0}
where
is regularly varying at zero of order (0 < < 1). Let be an inverse function of near zero such that (s)=(s) log log(1/s) is increasing near zero. We obtain exact estimates for the weak -variation of X(t) on [0,a]. 相似文献