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1.
For an irreducible symmetric Markov process on a (not necessarily compact) state space associated with a symmetric Dirichlet
form, we give Poincaré-type inequalities. As an application of the inequalities, we consider a time-inhomogeneous diffusion
process obtained by a time-dependent drift transformation from a diffusion process and give general conditions for the transience
or recurrence of some sets. As a particular case, the diffusion process appearing in the theory of simulated annealing is
considered. 相似文献
2.
J. C. Pardo 《Journal of Theoretical Probability》2009,22(2):514-542
We establish integral tests in connection with laws of the iterated logarithm at 0 and at +∞, for the upper envelope of positive
self-similar Markov processes. Our arguments are based on the Lamperti representation and on the study of the upper envelope
of the future infimum due to the author (see Pardo in Stoch. Stoch. Rep. 78:123–155, [2006]). These results extend laws of the iterated logarithm for Bessel processes due to Dvoretsky and Erdős (Proceedings of the
Second Berkeley Symposium, [1951]) and stable Lévy processes with no positive jumps conditioned to stay positive due to Bertoin (Stoch. Process. Appl. 55:91–100,
[1995]).
Research supported by a grant from CONACYT (Mexico). 相似文献
3.
Jean-Christophe Breton 《Journal of Theoretical Probability》2010,23(1):21-38
We investigate the regularity of shot noise series and of Poisson integrals. We give conditions for the absolute continuity
of their law with respect to the Lebesgue measure and for their continuity in total-variation norm. In particular, the case
of truncated series in addressed. Our method relies on a disintegration of the probability space based on a mere conditioning
by the first jumps of the underlying Poisson process. 相似文献
4.
In this paper, we findall metacyclic groups (a,b:am=e,bs=e,b-1ab=ar), where m=10,14,15,20,21,22, such that the cusp forms associated with all elements of these groups by an exact representation are multiplicative-products. We also consider the correspondence between multiplicative -products and elements of finite order in SL(5,C) by the adjoint representation. 相似文献
5.
Riesz products on the ring of p-adic integers are introduced and studied from the points of view of harmonic analysis and dynamical system relative to the
shift transformation. We find necessary and sufficient conditions for a Riesz product to be invariant, quasi-invariant or
quasi-Bernoulli. We study the mutual absolute continuity of two Riesz products and the almost everywhere convergence of lacunary
series with respect to a Riesz product. We also compute the Hausdorff dimension and the energy dimension and prove a multifractal
formalism for a given Riesz product. 相似文献
6.
Min Zhi ZHAO Hui Zeng ZHANG 《数学学报(英文版)》2007,23(1):111-126
Transience and recurrence are among the most important concepts in Markov processes. In this paper, we study the transience and recurrence for right processes with a given weight function, and characterize them by potentials, excessive functions, first hitting times and last exit times of the process. We also study the properties of recurrent states. 相似文献
7.
We introduce a deformed product construction for simple polytopes in terms of lower-triangular block matrix representations. We further show how Gale duality can be employed for the construction and the analysis of deformed products such that specified faces (e.g., all the k-faces) are “strictly preserved” under projection. Thus, starting from an arbitrary neighborly simplicial (d?2)-polytope Q on n?1 vertices, we construct a deformed n-cube, whose projection to the last d coordinates yields a neighborly cubical d -polytope. As an extension of the cubical case, we construct matrix representations of deformed products of (even) polygons (DPPs) which have a projection to d-space that retains the complete $(\lfloor\tfrac{d}{2}\rfloor-1)We introduce a deformed product construction for simple polytopes in terms of lower-triangular block matrix representations.
We further show how Gale duality can be employed for the construction and the analysis of deformed products such that specified
faces (e.g., all the k-faces) are “strictly preserved” under projection.
Thus, starting from an arbitrary neighborly simplicial (d−2)-polytope Q on n−1 vertices, we construct a deformed n-cube, whose projection to the last d coordinates yields a neighborly cubical
d
-polytope. As an extension of the cubical case, we construct matrix representations of deformed products of (even) polygons (DPPs)
which have a projection to d-space that retains the complete
(?\tfracd2?-1)(\lfloor\tfrac{d}{2}\rfloor-1)
-skeleton. 相似文献
8.
Lasse Leskelä 《Journal of Theoretical Probability》2010,23(2):523-546
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable
spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov processes,
it suffices that the generators of the processes preserve some, not necessarily reflexive or transitive, subrelation of the
order relation. The main contributions of the paper are: a functional characterization of stochastic relations, necessary
and sufficient conditions for the preservation of stochastic relations, and an algorithm for finding subrelations preserved
by probability kernels. The theory is illustrated with applications to hidden Markov processes, population processes, and
queueing systems. 相似文献
9.
We consider the asymptotic behavior of semi-stable Markov processes valued in ]0,[ when the starting point tends to 0. The entrance distribution is expressed in terms of the exponential functional of the underlying Lévy process which appears in Lamperti's representation of a semi-stable Markov process. 相似文献
10.
Set-valvedMarkovProcessesandTheirRepresentationTheoremsXuMingyue(徐明跃)(DepartmentofMathematics,HavenNormalUniversity,Harbin,15... 相似文献
11.
Hassen Ben Mohamed 《The Ramanujan Journal》2010,21(2):145-171
In this work, we consider the Jacobi-Dunkl operator Λ
α,β
,
a 3 b 3 \frac-12\alpha\geq\beta\geq\frac{-1}{2}
,
a 1 \frac-12\alpha\neq\frac{-1}{2}
, on ℝ. The eigenfunction
Yla,b\Psi_{\lambda}^{\alpha,\beta}
of this operator permits to define the Jacobi-Dunkl transform. The main idea in this paper is to introduce and study the Jacobi-Dunkl
transform and the Jacobi-Dunkl convolution product on new spaces of distributions 相似文献
12.
Nataliya V. Smorodina 《Acta Appl Math》2007,97(1-3):239-250
Let ξ(t),t∈[0,1] be a strictly stable Lévy process with the index of stability α∈(0,2). By ℘
ξ
we denote the law of ξ in the Skorokhod space
. For arbitrary ξ we construct ℘
ξ
-quasi-invariant semigroup of transformations of
. Under some nondegeneracy condition on the spectral measure of the stable process we construct ℘
ξ
-quasi-invariant group of transformations of
. In symmetric case this group is a group of the invariant transformations.
相似文献
13.
14.
15.
Géza Tóth 《Discrete and Computational Geometry》2008,39(4):791-799
The crossing number
of a graph G is the minimum possible number of edge-crossings in a drawing of G, the pair-crossing number
is the minimum possible number of crossing pairs of edges in a drawing of G, and the odd-crossing number
is the minimum number of pairs of edges that cross an odd number of times. Clearly,
. We construct graphs with
. This improves the bound of Pelsmajer, Schaefer and Štefankovič. Our construction also answers an old question of Tutte.
Slightly improving the bound of Valtr, we also show that if the pair-crossing number of G is k, then its crossing number is at most O(k
2/log 2
k).
G. Tóth’s research was supported by the Hungarian Research Fund grant OTKA-K-60427 and the Research Foundation of the City
University of New York. 相似文献
16.
ConsidertheDiracspectralproblemwherep,qaretwopotentials,Aisaspectralparameter.L*isaninjectivehomomorphism.ThefunctionalgradientVA=(2RR,ri-of)TofeigenvalueAwithrespecttop,qsatisfiesarecalledtheLenard'soperatorpairof(1).Theorem1LetG(1)(x),G(z)(x)betwoarbitarysmoothfunctions,G=(G(1),G(2))".ThenthefollowingoperatorequationwithrespecttoV=V(G),possessestheoperatorsolutionwhereL.'-jisthecommutator;L=L(p,q),K,Jaredefinedby(1)l(4)respectively.ProofSubstitute(6)into(5),directlycalculate.Defin… 相似文献
17.
Pseudo-differential and Fourier series operators on the torus
\mathbbTn=(\BbbR/2p\BbbZ)n{{\mathbb{T}}^{n}}=(\Bbb{R}/2\pi\Bbb{Z})^{n}
are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal
symbols are investigated and the correspondence between toroidal and Euclidean symbols of pseudo-differential operators is
established. Periodization of operators and hyperbolic partial differential equations is discussed. Fourier series operators,
which are analogues of Fourier integral operators on the torus, are introduced, and formulae for their compositions with pseudo-differential
operators are derived. It is shown that pseudo-differential and Fourier series operators are bounded on L
2 under certain conditions on their phases and amplitudes. 相似文献
18.
In this paper we study sequences of vector orthogonal polynomials. The vector orthogonality presented here provides a reinterpretation
of what is known in the literature as matrix orthogonality. These systems of orthogonal polynomials satisfy three-term recurrence
relations with matrix coefficients that do not obey to any type of symmetry. In this sense the vectorial reinterpretation
allows us to study a non-symmetric case of the matrix orthogonality. We also prove that our systems of polynomials are indeed
orthonormal with respect to a complex measure of orthogonality. Approximation problems of Hermite-Padé type are also discussed.
Finally, a Markov’s type theorem is presented. 相似文献
19.
Potential Analysis - The upper escape rate for a Markov process is a natural partial generalization of the celebrated Khintchine’s law of the iterated logarithm. In this article, we present a... 相似文献
20.
Mean-value theorems and extensions of the Elliott-Daboussi theorem on additive arithmetic semigroups
Wen-Bin Zhang 《The Ramanujan Journal》2008,15(1):47-75
We present more general forms of the mean-value theorems established before for multiplicative functions on additive arithmetic
semigroups and prove, on the basis of these new theorems, extensions of the Elliott-Daboussi theorem. Let
be an additive arithmetic semigroup with a generating set ℘ of primes p. Assume that the number G(m) of elements a in
with “degree” ∂(a)=m satisfies
with constants q>1, ρ
1<ρ
2<⋅⋅⋅<ρ
r
=ρ, ρ≥1, γ>1+ρ. For the main result, let α,τ,η be positive constants such that α>1,τ
ρ≥1, and τ
α
ρ≥1. Then for a multiplicative function f(a) on
the following two conditions (A) and (B) are equivalent. These are (A) All four series
converge and
and (B) The order τ
ρ mean-value
exists with m
f
≠0 and the limit
exists with M
v
(α)>0.
相似文献