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1.
Let
be sequences of real numbers which are symmetric in k. Let
be independent sequences of independent normal random variables with mean zero and variance one. For each fixed choice of
we consider
Let
Several examples are given in which the condition
is either a sufficient, a necessary, or a necessary and sufficient condition for {Q(x), x[0, 2]
n
} to have a continuous version. 相似文献
2.
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
3.
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
4.
Bhagat Singh 《Czechoslovak Mathematical Journal》2000,50(3):627-639
Qualitative comparison of the nonoscillatory behavior of the equations
and
is sought by way of finding different nonoscillation criteria for the above equations, L
n is a disconjugate operator of the form
Both canonical and noncanonical forms of L
n have been studied. 相似文献
5.
Asymptotic properties of partitions of the unit interval are studied through the entropy for random partition
where
are the order statistics of a random sample {X
i, i n}, X
0, n
–, X
n+1, n
+ and F(x) is a continuous distribution function. A characterization of continuous distributions based on
is obtained. Namely, a sequence of random observations {X
i, i1} comes from a continuous cumulative distribution function (cdf) F(x) if and only if
where = 0.577 is Euler's constant. If {X
i, i1} come from a density g(x) and F is a cdf with density f(x), some limit theorems for
are established, e.g.,
Statistical estimation as well as a goodness-of-fit test based on
are also discussed. 相似文献
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6.
Claude L. Schochet 《K-Theory》1998,14(2):197-199
In this note we correct a mistake in K-Theory 10 (1996), 49–72. In that paper we asserted that under bootstrap hypotheses the short exact sequence
which arises in the computation ofKK(A,B)
(is a split sequence. This is not always the case. ThusKK(A,B)
(decomposes into the three components
and
However, this is a decomposition in the sense of composition series, not as three direct summands. The same correction applies to the Milnor sequence. If there is no primepfor which bothK(A)
(andK(B)
*haveptorsion then the decomposition is indeed as direct summands. The other results of the paper are unaffected. 相似文献
7.
For a given map
defined on the field
of p-adic numbers satisfying
for some integer r, a Markov process on
induced by the map ϕ is constructed in (Kaneko and Zhao (1994) Forum Math. J. 16, 69). This approach can still be our choice in constructing a Markov process on finite algebraic extension of
. We will give an answer to the question as to how Markov process driven by set of maps will be addressed. Especially, we will focus on case the maps are given by the elements of Galois group of the extension. 相似文献
8.
Hrvoje Šikić 《Journal of Theoretical Probability》2000,13(2):571-574
We prove that for a>0, (B
t) one-dimensional standard Brownian motion and
0=inf{t>0 : B
t=0} the following zero–one law is valid
相似文献
9.
Goran Peskir 《Journal of Theoretical Probability》2001,14(3):845-855
Let X=(X
t
)
t0 be a one-dimensional time-homogeneous diffusion process associated with the infinitesimal generator
where x(x) and x(x)>0 are continuous. We show how the question of finding a function xH(x) such that
holds for all stopping times of X relates to solutions of the equation:
Explicit expressions for H are derived in terms of and . The method of proof relies upon a domination principle established by Lenglart and Itô calculus. 相似文献
10.
Let K, D be n-dimensional convex bodes. Define the distance between K and D as
where the infimum is taken over all
and all invertible linear operators T. Assume that 0 is an interior point of K and define
where is the uniform measure on the sphere. We use the difference body estimate to prove that K can be embedded into
so that
for some absolute constants C and
. We apply this result to show that the distance between two n-dimensional convex bodies does not exceed
up to a logarithmic factor. 相似文献
11.
Let
be realhomogeneous functions in
ofdegree
and let bethe Borel measure on
given by
where dx denotes theLebesgue measure on
and > 0. Let T
be the convolution operator
and let
Assume that, for x 0, the followingtwo conditions hold:
vanishes only at h = 0 and
. In this paper we show that if
then E
is the empty set and if
then E
is the closed segment withendpoints
and
. Also, we give some examples. 相似文献
12.
Sufficient conditions are established for the oscillation of proper solutions of the system
where f
i
:+ × 2m (i=1,2) satisfy the local Carathéodory conditions and
i
,
i
:+ +(i=1,...,m) are continuous functions such that
i
(t) t for
. 相似文献
13.
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
14.
M. J. Appel 《Journal of Theoretical Probability》2002,15(1):153-159
Birkhoff's well-known ergodic theorem states that the simple averages of a sequence of real (integrable) function values on successive iterates of a measure-preserving mapping T converge a.s. to the conditional expected value of the function conditioned on the invariant sigma-field. If the mapping is in addition ergodic, then the limit is simply the unconditional expected value:
In this article, we discuss the analogous result for sequences of partial maxima: given a measurable f, if T is measure-preserving and ergodic then
Series criteria are provided which characterize the a.s. maximal and minimal growth rates of the sequence of partial maxima. 相似文献
15.
Aurel Spătaru 《Journal of Theoretical Probability》1999,12(3):811-819
Let X, X
1, X
2,... be a sequence of i.i.d. random variables such that EX=0, assume the distribution of X is attracted to a stable distribution with exponent <1, and set S
n=X
1+ ··· +X
n. We prove that
相似文献
16.
A differential calculus for random fields is developed and combined with the S-transform to obtain an explicit strong solution of the Cauchy problem
Here L is a linear second order elliptic operator, hi and c are real functions, and
, where W
t
is a Brownian motion. An application of the solution to nonlinear filtering and mathematical finance is also considered. 相似文献
17.
Anthony J. D'Aristotile 《Journal of Theoretical Probability》1995,8(2):321-346
LetX be the collection ofk-dimensional subspaces of ann-dimensional vector spaceV
n overGF(q). A metric may be defined onX by letting
|
相似文献
18.
Ram U. Verma 《Journal of Computational Analysis and Applications》2002,4(3):177-192
Consider the convergence of the projection methods based on an extension of a special class of algorithms for the approximation--solvability of the following class of nonlinear quasivariational inequality (NQVI) problems: find an element
such that
and
19.
Miguel A. Arcones 《Journal of Theoretical Probability》1999,12(3):615-641
Let {X
j
}
j = 1
be a stationary Gaussian sequence of random vectors with mean zero. We give sufficient conditions for the compact law of the iterate logarithm of
20.
A. Cabot 《Journal of Optimization Theory and Applications》2004,120(2):275-303
Let H be a real Hilbert space and let
be a
function that we wish to minimize. For any potential
and any control function
which tends to zero as t+, we study the asymptotic behavior of the trajectories of the following dissipative system:
|