共查询到20条相似文献,搜索用时 15 毫秒
1.
Hans-Peter Scheffler 《Probability Theory and Related Fields》2000,116(2):257-271
For a random vector belonging to the (generalized) domain of operator semistable attraction of some nonnormal law we prove
various variants of Chover's law of the iterated logarithm for the partial sum. Furthermore we also derive some large deviation
results necessary for the proof of our main theorems.
Received: 30 September 1998 / Revised version: 28 May 1999 相似文献
2.
Let X
i
, i∈N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φ be a mapping B→R. Under a central limit theorem assumption, an asymptotic evaluation of Z
n
= E (exp (n
Φ (∑
i
=1
n
X
i
/n))), up to a factor (1 + o(1)), has been gotten in Bolthausen [1]. In this paper, we show that the same asymptotic evaluation can be gotten without
the central limit theorem assumption.
Received: 19 September 1997 / Revised version:22 April 1999 相似文献
3.
We prove the existence of a unique solution for a one-dimensional stochastic parabolic partial differential equation with
random and adapted coefficients perturbed by a two-parameter white noise. The proof is based on a maximal inequality for the
Skorohod integral deduced from It?'s formula for this anticipating stochastic integral.
Received: 21 November 1997 / Revised version: 20 July 1998 相似文献
4.
M. Kappert 《Numerische Mathematik》1996,74(4):397-417
Summary. Let denote the -th partial sum of the exponential function. Carpenter et al. (1991) [1] studied the exact rate of convergence of the zeros
of the normalized partial sums to the so-called Szeg?-curve Here we apply parts of the results found by Carpenter et al. to the zeros of the normalized partial sums of and .
Received August 11, 1995 相似文献
5.
David Steinsaltz 《Probability Theory and Related Fields》1997,107(1):99-121
Summary. A self-modifying random walk on is derived from an ordinary random walk on the integers by interpolating a new vertex into each edge as it is crossed. This
process converges almost surely to a random variable which is totally singular with respect to Lebesgue measure, and which
is supported on a subset of having Hausdorff dimension less than , which we calculate by a theorem of Billingsley. By generating function techniques we then calculate the exponential rate
of convergence of the process to its limit point, which may be taken as a bound for the convergence of the measure in the
Wasserstein metric. We describe how the process may viewed as a random walk on the space of monotone piecewise linear functions,
where moves are taken by successive compositions with a randomly chosen such function.
Received: 20 November 1995 / In revised form: 14 May 1996 相似文献
6.
Jérôme Dedecker 《Probability Theory and Related Fields》1998,110(3):397-426
Summary. We prove a central limit theorem for strictly stationary random fields under a projective assumption. Our criterion is similar
to projective criteria for stationary sequences derived from Gordin's theorem about approximating martingales. However our
approach is completely different, for we establish our result by adapting Lindeberg's method. The criterion that it provides
is weaker than martingale-type conditions, and moreover we obtain as a straightforward consequence, central limit theorems
for α-mixing or φ-mixing random fields.
Received: 19 February 1997 / In revised form: 2 September 1997 相似文献
7.
Summary. We study here in detail the location of the real and complex zeros of the partial sums of and , which extends results of Szeg? (1924) and Kappert (1996). Received November 9, 2000 / Published online August 17, 2001 相似文献
8.
Suppose K is a compact convex set in ℝ2 and X
i
, 1≤i≤n, is a random sample of points in the interior of K. Under general assumptions on K and the distribution of the X
i
we study the asymptotic properties of certain statistics of the convex hull of the sample.
Received: 24 July 1996/Revised version: 24 February 1998 相似文献
9.
E.M. Rains 《Probability Theory and Related Fields》1997,107(2):219-241
Summary. If a random unitary matrix is raised to a sufficiently high power, its eigenvalues are exactly distributed as independent, uniform phases. We prove
this result, and apply it to give exact asymptotics of the variance of the number of eigenvalues of falling in a given arc, as the dimension of tends to infinity. The independence result, it turns out, extends to arbitrary representations of arbitrary compact Lie groups.
We state and prove this more general theorem, paying special attention to the compact classical groups and to wreath products.
This paper is excerpted from the author's doctoral thesis, [9].
Received: 15 October 1995 / In revised form: 7 March 1996 相似文献
10.
In this paper we study the well-posedness and regularity of the adapted solutions to a class of linear, degenerate backward stochastic partial differential equations (BSPDE, for short). We establish new
a priori estimates for the adapted solutions to BSPDEs in a general setting, based on which the existence, uniqueness, and regularity
of adapted solutions are obtained. Also, we prove some comparison theorems and discuss their possible applications in mathematical
finance.
Received: 24 September 1997 / Revised version: 3 June 1998 相似文献
11.
Vydas Čekanavičius 《Probability Theory and Related Fields》1998,111(4):565-583
For lattice distributions a convolution of two signed Poisson measures proves to be an approximation comparable with the
normal law. It enables to get rid of cumbersome summands in asymptotic expansions and to obtain estimates for all Borel sets.
Asymptotics can be constructed two-ways: by adding summands to the leading term or by adding summands in its exponent. The
choice of approximations is confirmed by the Ibragimov-type necessary and sufficient conditions.
Received: 20 November 1996 / Revised version: 5 December 1997 相似文献
12.
We prove that the process of the most visited site of Sinai's simple random walk in random environment is transient. The
rate of escape is characterized via an integral criterion. Our method also applies to a class of recurrent diffusion processes
with random potentials. It is interesting to note that the corresponding problem for the usual symmetric Bernoulli walk or
for Brownian motion remains open.
Received: 17 April 1998 相似文献
13.
Raoul LePage Krzysztof Podgórski Michał Ryznar 《Probability Theory and Related Fields》1997,108(2):281-298
Summary. We prove almost sure convergence of a representation of normalized partial sum processes of a sequence of i.i.d. random variables
from the domain of attraction of an α-stable law, α<2. We obtain an explicit form of the limit in terms of the LePage series representation of stable laws. One consequence of
these results is a conditional invariance principle having applications to option pricing as well as to resampling by signs and permutations.
Received: 11 April 1994 / In revised form: 5 November 1996 相似文献
14.
Eric M. Rains 《Probability Theory and Related Fields》1998,112(3):411-423
Using the machinery of zonal polynomials, we examine the limiting behavior of random symmetric matrices invariant under conjugation
by orthogonal matrices as the dimension tends to infinity. In particular, we give sufficient conditions for the distribution
of a fixed submatrix to tend to a normal distribution. We also consider the problem of when the sequence of partial sums of
the diagonal elements tends to a Brownian motion. Using these results, we show that if O
n
is a uniform random n×n orthogonal matrix, then for any fixed k>0, the sequence of partial sums of the diagonal of O
k
n
tends to a Brownian motion as n→∞.
Received: 3 February 1998 / Revised version: 11 June 1998 相似文献
15.
Self-decomposable distributions are given as limits of normalized sums of independent random variables. We define semi-selfdecomposable
distributions as limits of subsequences of normalized sums. More generally, we introduce a way of making a new class of limiting
distributions derived from a class of distributions by taking the limits through subsequences of normalized sums, and define
the class of semi-selfdecomposable distributions and a decreasing sequence of subclasses of it. We give two kinds of necessary
and sufficient conditions for distributions belonging to those classes, one is in terms of the decomposability of random variables
and another is in terms of Lévy measures.
Received: 1 May 1997 / Revised version: 5 February 1998 相似文献
16.
Ji-guang Sun 《Numerische Mathematik》1995,69(3):373-382
Summary.
This paper is a continuation of the author [6] in Numerische
Mathematik.
Let be a nondefective multiple eigenvalue of
multiplicity
of an complex matrix , and let
be the
secants of the canonical
angles between the left and right invariant subspaces of
corresponding to the multiple eigenvalue . The analysis
of this paper shows that the quantities
are the worst-case condition numbers of the multiple eigenvalue
.
Received September 28, 1992 / Revised version
received January 18, 1994 相似文献
17.
R. A. Doney 《Probability Theory and Related Fields》1997,107(4):451-465
Summary. If {S
n
,n≧0} is an integer-valued random walk such that S
n
/a
n
converges in distribution to a stable law of index α∈ (0,1) as n→∞, then Gnedenko’s local limit theorem provides a useful estimate for P{S
n
=r} for values of r such that r/a
n
is bounded. The main point of this paper is to show that, under certain circumstances, there is another estimate which is
valid when r/a
n
→ +∞, in other words to establish a large deviation local limit theorem. We also give an asymptotic bound for P{S
n
=r} which is valid under weaker assumptions. This last result is then used in establishing some local versions of generalized
renewal theorems.
Received: 9 August 1995 / In revised form: 29 September 1996 相似文献
18.
Alexander D. Wentzell 《Probability Theory and Related Fields》1999,113(2):255-271
. For a certain class of families of stochastic processes ηε(t), 0≤t≤T, constructed starting from sums of independent random variables, limit theorems for expectations of functionals F(ηε[0,T]) are proved of the form
where w
0 is a Wiener process starting from 0, with variance σ2 per unit time, A
i
are linear differential operators acting on functionals, and m=1 or 2. Some intricate differentiability conditions are imposed on the functional.
Received: 12 September 1995 / Revised version: 6 April 1998 相似文献
19.
20.
Daniel Neuenschwander 《Monatshefte für Mathematik》2000,129(2):133-137
We prove unimodality of all dilatation-stable Gaussian laws on the Heisenberg group. (Received 23 March 1998; in final form 19 May 1999) 相似文献