共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
Ioannis Kontoyiannis 《Journal of Theoretical Probability》1998,11(3):795-811
Let
be a discrete-valued stationary ergodic process distributed according to P and let x=(..., x
–1, x
0, x
1,...) denote a realization from X. We investigate the asymptotic behavior of the recurrence time R
n defined as the first time that the initial n-block
reappears in the past of x. We identify an associated random walk,
on the same probability space as X, and we prove a strong approximation theorem between log R
n and
. From this we deduce an almost sure invariance principle for log R
n. As a byproduct of our analysis we get unified proofs for several recent results that were previously established using methods from ergodic theory, the theory of Poisson approximation and the analysis of random trees. Similar results are proved for the waiting time W
n defined as the first time until the initial n-block from one realization first appears in an independent realization generated by the same (or by a different) process. 相似文献
3.
Let u(x) xR
q
be a symmetric nonnegative definite function which is bounded outside of all neighborhoods of zero but which may have u(0)=. Let p
x, (·) be the density of an R
q
valued canonical normal random variable with mean x and variance and let {G
x, ; (x, )R
q
×[0,1 ]} be the mean zero Gaussian process with covariance
A finite positive measure on R
q
is said to be in
with respect to u, if
When
, a multiple Wick product chaos
is defined to be the limit in L
2, as 0, of
where
,
denotes the Wick product of the m
j
normal random variables
.Consider also the associated decoupled chaos processes
,
defined as the limit in L
2, as 0, of
where
are independent copies of G
x,.Define
Note that a neighborhood of the diagonals of
in
is excluded, except those points on the diagonal which originate in the same Wick product in (i). Set
One of the main results of this paper is:
Theorem A. If
is continuous on (R
q
)
r
for all
then
is continuous on
.When u satisfies some regularity conditions simple sufficient conditions are obtained for the continuity of
on (R
q
)
r
. Also several variants of (i) are considered and related to different types of decoupled processes. These results have applications in the study of intersections of Lévy process and continuous additive functionals of several Lévy processes. 相似文献
4.
Let X,
,X
1,...,X
n
be i.i.d. random variables taking values in a measurable space (
). Consider U-statistics of degree two
with symmetric, degenerate kernel
. Let
where {q
j
} are eigenvalues of the Hilbert–Schmidt operator associated with the kernel and {
j
} are i.i.d. standard normal random variables. If
then
Upper bounds for
n
are established under the moment condition
, provided that at least thirteen eigenvalues of the operator do not vanish. In Theorem 1.1 the bound is expressed via terms containing tail and truncated moments. The proof is based on the method developed by Bentkus and Götze.(1) 相似文献
5.
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
6.
L. Wu 《Journal of Theoretical Probability》2004,17(4):967-978
For an exchangeable sequence of random variables
valued in a Polish space, we obtain a necessary and sufficient condition for the large deviation principles of the occupation measure L
n
:=(1/n)
and of the process-level empirical measures. 相似文献
7.
We construct a metric space of set functions (
, d) such that a sequence {P
n} of Borel probability measures on a metric space (
, d*) satisfies the full Large Deviation Principle (LDP) with speed {a
n} and good rate function I if and only if the sequence
converges in (
, d) to the set function e
–I
. Weak convergence of probability measures is another special case of convergence in (
, d). Properties related to the LDP and to weak convergence are then characterized in terms of (
, d). 相似文献
8.
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
9.
10.
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
11.
Let X
t be a one-dimensional diffusion of the form dX
t=dB
t+(X
t)dt. Let Tbe a fixed positive number and let
be the diffusion process which is X
t conditioned so that X
0=X
T=x. If the drift is constant, i.e.,
, then the conditioned diffusion process
is a Brownian bridge. In this paper, we show the converse is false. There is a two parameter family of nonlinear drifts with this property. 相似文献
12.
Matthew Harris 《Journal of Theoretical Probability》2001,14(2):299-317
We consider a Poisson point process on
with intensity , and at each Poisson point we place a two sided mirror of random length and orientation. The length and orientation of a mirror is taken from a fixed distribution, and is independent of the lengths and orientations of the other mirrors. We ask if light shone from the origin will remain in a bounded region. We find that there exists a
with 0 <
< for which, if
<
, light leaving the origin in all but a countable number of directions will travel arbitrariliy far from the origin with positive probability. Also, if
>
, light from the origin will almost surely remain in a bounded region. 相似文献
13.
Using an analog of the classical Frobenius recursion, we define the notion of a Frobenius
-homomorphism. For
, this is an ordinary ring homomorphism. We give a constructive proof of the following theorem. Let X be a compact Hausdorff space,
the
th symmetric power of X, and
the algebra of continuous complex-valued functions on X with the sup-norm; then the evaluation map
defined by the formula
identifies the space
with the space of all Frobenius
-homomorphisms of the algebra
into
with the weak topology. 相似文献
14.
We prove that the Sobolev embedding operator S
d,k,p :
, where 1/s=1/p-k/d , is (v,1) -absolutely summing for appropriate v > 1 . The result is optimal for s
2 . 相似文献
15.
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
16.
We study the problem of representation of a homogeneous semigroup {
t
}
t 0 of transformations of probability measures on
in the form
where
satisfies a differential equation of a special form dependent on the measure . We give necessary and sufficient conditions for this representation. 相似文献
17.
L. Yu. Cherednikova 《Mathematical Notes》2005,77(5-6):715-725
Suppose that
is a system of continuous subharmonic functions in the unit disk
and
is the class of holomorphic functions f in
such that log|f(z)| ≤ B
f
p
f
(z) + C
f
, z ∈
, where B
f
and C
f
are constants and p
f
∈
. We obtain sufficient conditions for a given number sequence Λ = { λn} ⊂
to be a subsequence of zeros of some nonzero holomorphic function from
, i.e., Λ is a nonuniqueness sequence for
.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 775–787.Original Russian Text Copyright ©2005 by L. Yu. Cherednikova. 相似文献
18.
19.
We consider the Skyrme model using the explicit parameterization of the rotation group
through elements of its algebra. Topologically nontrivial solutions already arise in the one-dimensional case because the fundamental group of
is
. We explicitly find and analyze one-dimensional static solutions. Among them, there are topologically nontrivial solutions with finite energy. We propose a new class of projective models whose target spaces are arbitrary real projective spaces
. 相似文献
20.
Let
be i.i.d. random variables and let, for each
and
. It is shown that
a.s. whenever the sequence of self-normalized sums S
n
/V
n is stochastically bounded, and that this limsup is a.s. positive if, in addition, X is in the Feller class. It is also shown that, for X in the Feller class, the sequence of self-normalized sums is stochastically bounded if and only if
相似文献