共查询到20条相似文献,搜索用时 125 毫秒
1.
Henri Heinich 《Journal of Theoretical Probability》2006,19(2):509-534
In this paper, we generalize the Kantorovich functional to K?the-spaces for a cost or a profit function. We examine the convergence
of probabilities with respect to this functional for some K?the-spaces. We study the Monge problem: Let
be a K?the-space, P and Q two Borel probabilities defined on a Polish space M and a cost function
. A K?the functional
is defined by
(P, Q) = inf
where
is the law of X. If c is a profit function, we note
. (P, Q) = sup
Under some conditions, we show the existence of a Monge function, φ, such that
, or
.
相似文献
2.
Michele Baldini 《Journal of Theoretical Probability》2007,20(1):65-86
Given a one-dimensional positive recurrent diffusion governed by the Stratonovich SDE , we show that the associated stochastic flow of diffeomorphisms focuses as fast as , where is the finite stationary measure. Moreover, if the drift is reversed and the diffeomorphism is inverted, then the path function
so produced tends, independently of its starting point, to a single (random) point whose distribution is . Applications to stationary solutions of X
t
, asymptotic behavior of solutions of SPDEs and random attractors are offered.
This paper was written while the author was visiting Northwestern University and the opinions expressed in it are those of
the author alone and do not necessarily reflect the views of Merrill Lynch, its subsidiaries or affiliates. 相似文献
3.
Leonid Bogachev 《Journal of Theoretical Probability》2006,19(4):849-873
We are concerned with the limit distribution of l
t
-norms (of order t) of samples of i.i.d. positive random variables, as N→∞, t→∞. The problem was first considered by Schlather [(2001), Ann. Probab. 29, 862–881], but the case where {X
i
} belong to the domain of attraction of Gumbel’s double exponential law (in the sense of extreme value theory) has largely
remained open (even for an exponential distribution). In this paper, it is assumed that the log-tail distribution function
is regularly varying at infinity with index . We proceed from studying the limit distribution of the sums , which is of interest in its own right. A proper growth scale of N relative to t appears to be of the form (). We show that there are two critical points, α1 = 1 and α2 = 2, below which the law of large numbers and the central limit theorem, respectively, break down. For α < 2, under a slightly
stronger condition of normalized regular variation of h, we prove that the limit laws for S
N
(t) are stable, with characteristic exponent and skewness parameter . A complete picture of the limit laws for the norms R
N
(t) = S
N
(t)1/t
is then derived. In particular, our results corroborate a conjecture in Schlather [(2001), Ann. Probab. 29, 862–881] regarding the “endpoints” , α→ 0.
相似文献
4.
Andrew Raich 《Mathematische Zeitschrift》2007,256(1):193-220
Let be a subharmonic, nonharmonic polynomial and a parameter. Define , a closed, densely defined operator on . If and , we solve the heat equations , u(0,z) = f(z) and , . We write the solutions via heat semigroups and show that the solutions can be written as integrals against distributional
kernels. We prove that the kernels are C
∞ off of the diagonal {(s, z, w) : s = 0 and z = w} and find pointwise bounds for the kernels and their derivatives.
相似文献
5.
Let
be a continuous semimartingale and let
be a continuous function of bounded variation. Setting
and
suppose that a continuous function
is given such that F is C1,2 on
and F is
on
. Then the following change-of-variable formula holds:
where
is the local time of X at the curve b given by
and
refers to the integration with respect to
. A version of the same formula derived for an Itô diffusion X under weaker conditions on F has found applications in free-boundary problems of optimal stopping. 相似文献
6.
In this paper, we introduce the class of
-stopping lines which generalize the planar stopping lines in Merzbach [(1980), Stochastic Process. Appl. 10, 49–63] by replacing the positive quadrant of the plane by a collection
of compact subsets of a fixed topological space. Our notion of stopping line also compliments and generalizes the stopping
sets defined in Ivanoff and Merzbach [(1995), Stochastic Process. Appl. 57, 83–98].
相似文献
7.
Pavel Drábek Peter Takáč 《Calculus of Variations and Partial Differential Equations》2007,29(1):31-58
An improved Poincaré inequality and validity of the Palais-Smale condition are investigated for the energy functional on , 1 < p < ∞, where Ω is a bounded domain in , is a spectral (control) parameter, and is a given function, in Ω. Analysis is focused on the case λ = λ1, where −λ1 is the first eigenvalue of the Dirichlet p-Laplacian Δ
p
on , λ1 > 0, and on the “quadratization” of within an arbitrarily small cone in around the axis spanned by , where stands for the first eigenfunction of Δ
p
associated with −λ1. 相似文献
8.
Aimé Lachal 《Journal of Theoretical Probability》2006,19(4):757-771
Let (B
t
)
t≥ 0 be standard Brownian motion starting at y and set X
t
= for , with V(y) = y
γ if y≥ 0, V(y) = −K(−y)γ if y≤ 0, where γ and K are some given positive constants. Set . In this paper, we provide some formulas for the probability distribution of the random variable as well as for the probability (or b)}. The formulas corresponding to the particular cases x = a or b are explicitly expressed by means of hypergeometric functions.
相似文献
9.
Jun Zhang 《Annals of the Institute of Statistical Mathematics》2007,59(1):161-170
The family of α-connections ∇(α) on a statistical manifold equipped with a pair of conjugate connections and is given as . Here, we develop an expression of curvature R
(α) for ∇(α) in relation to those for . Immediately evident from it is that ∇(α) is equiaffine for any when are dually flat, as previously observed in Takeuchi and Amari (IEEE Transactions on Information Theory 51:1011–1023, 2005). Other related formulae are also developed.
The work was conducted when the author was on sabbatical leave as a visiting research scientist at the Mathematical Neuroscience
Unit, RIKEN Brain Science Institute, Wako-shi, Saitama 351-0198, Japan. 相似文献
10.
Mika Hujo 《Journal of Theoretical Probability》2006,19(1):190-203
For a Borel-function
, we consider the approximation of a random variable f(W
1) with
by stochastic integrals with respect to the Brownian motion
and the geometric Brownian motion, where the integrands are piecewise constant within certain deterministic time intervals. In earlier papers it has been shown that under certain regularity conditions the optimal approximation rate is 1/
, if one optimizes over deterministic time-nets of cardinality n. We will show the existence of random variables f(W
1) such that the approximation error tends as slowly to zero as one wishes. 相似文献
11.
Alexander J. Zaslavski 《Calculus of Variations and Partial Differential Equations》2007,28(3):351-381
In this paper we study nonoccurrence of the Lavrentiev phenomenon for a large class of nonconvex nonautonomous constrained
variational problems. A state variable belongs to a convex subset of a Banach space with nonempty interior. Integrands belong
to a complete metric space of functions
which satisfy a growth condition common in the literature and are Lipschitzian on bounded sets. In our previous work Zaslavski
(Ann. Inst. H. Poincare, Anal. non lineare, 2006) we considered a class of nonconstrained variational problems with integrands
belonging to a subset
and showed that for any such integrand the infimum on the full admissible class is equal to the infimum on a subclass of
Lipschitzian functions with the same Lipschitzian constant. In the present paper we show that if an integrand f belongs to
, then this property also holds for any integrand which is contained in a certain neighborhood of f in
. Using this result we establish nonoccurrence of the Lavrentiev phenomenon for most elements of
in the sense of Baire category.
相似文献
12.
Michael Falk 《Extremes》2006,9(1):63-68
It is known that a bivariate extreme value distribution (EVD) with reverse exponential margins can be represented as , , where is a suitable norm on . We prove in this paper the converse implication, i.e., given an arbitrary norm on , , , defines an EVD with reverse exponential margins, if and only if the norm satisfies for the condition . This result is extended to bivariate EVDs with arbitrary margins as well as to extreme value copulas. By identifying an EVD , , with the unit ball corresponding to the generating norm , we obtain a characterization of the class of EVDs in terms of compact and convex subsets of . 相似文献
13.
Let be a nonstandard model of Peano Arithmetic with domain M and let be nonstandard. We study the symmetric and alternating groups S
n
and A
n
of permutations of the set internal to , and classify all their normal subgroups, identifying many externally defined such normal subgroups in the process. We provide
evidence that A
n
and S
n
are not split extensions by these normal subgroups, by showing that any such complement if it exists, cannot be a limit of
definable sets. We conclude by identifying an -valued metric on and (where B
S
, B
A
are the maximal normal subgroups of S
n
and A
n
identified earlier) making these groups into topological groups, and by showing that if is -saturated then and are complete with respect to this metric.
相似文献
14.
Consider a differential inclusion under state constraints
where is an unbounded set-valued map with closed and convex images, which is measurable in and -Lipschitz in (with ) and is a closed set with smooth boundary. We provide sufficient conditions for the set-valued map associating to each initial point the set of all solutions to the above constrained differential inclusion starting at to be pseudo-Lipschitz on . This result is applied to investigate local Lipschitz continuity of the value function for the constrained Bolza problem
of optimal control theory.
Work supported in part by the European Community's Human Potential Programme under contract HPRN-CT-2002-00281, Evolution
Equations. 相似文献
15.
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
16.
Yuan Zhang 《Mathematische Annalen》2007,337(2):457-478
Let
and
denote the complexifications of Heisenberg hypersurfaces in
and
, respectively. We show that non-degenerate holomorphic Segre mappings from
into
with
possess a partial rigidity property. As an application, we prove that the holomorphic Segre non-transversality for a holomorphic Segre map from
into
with
propagates along Segre varieties. We also give an example showing that this propagation property of holomorphic Segre transversality fails when N > 2n − 2. 相似文献
17.
Arvind Singh 《Journal of Theoretical Probability》2007,20(2):153-166
We consider a diffusion process X in a random potential of the form , where is a positive drift and is a strictly stable process of index with positive jumps. Then the diffusion is transient and converges in law towards an exponential distribution. This behaviour contrasts with the case where is a drifted Brownian motion and provides an example of a transient diffusion in a random potential which is as “slow” as
in the recurrent setting.
相似文献
18.
Let
be the Poisson point process with intensity 1 in Rd and let
be
. We obtain a strong invariance principle for the total length of the nearest-neighbor graph on
. 相似文献
19.
We prove a Γ-convergence result for the family of functionals defined on H
1(Ω) by for a given and a parameter . We show that in either of the two cases, p = 2 or , any limit of the minimizers is an optimal lifting. 相似文献
20.
The difference in length between two distinct factorizations of an element in a Dedekind domain or in the corresponding block
monoid is an object of study in the theory of non-unique factorizations. It provides an alternate way, distinct from what
the elasticity provides, of measuring the degree of non-uniqueness of factorizations. In this paper, we discuss the difference
in consecutive lengths of irreducible factorizations in block monoids of the form where . We will show that the greatest integer r, denoted by , which divides every difference in lengths of factorizations in can be immediately determined by considering the continued fraction of . We then consider the set including necessary and sufficient conditions (which depend on p) for a value to be an element of .
2000 Mathematics Subject Classification Primary—20M14, 11A55, 20D60, 11A51
Parts of this work are contained in the first author’s Doctoral Dissertation written at the University of North Carolina at
Chapel Hill under the direction of the third author. 相似文献