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给出了一般状态空间正则跳过程的定义,通过跳过程的比较定理,证明了一般状态空间跳过程正则性的两个等价条件:矩条件和漂移条件. 相似文献
3.
Markov chain approximations of reversible jump processes are investigated. Tightness results and a central limit theorem are
established. Moreover, given the generator of a reversible jump process with state space ℝ
d
, the approximating Markov chains are constructed explicitly. As a byproduct we obtain a definition of the Sobolev space H
α/2(ℝ
d
), α∈(0,2), that is equivalent to the standard one.
相似文献
4.
设μ=(μ_i)_i≥0为Z_+上的测度且p 1,考虑下述离散型p次Dirichlet型D_p(f)=Σ_(i=0)~∞μ_ib_i(f_i-f_(i+1))(f_i~(p-1)-f_(i+1)~(p-1)),f≥0,其中(b_i)_(i≥0)为Z_+上的正序列.本文旨在给出空间L~p(μ)上p次Dirichlet型D_p(f)所对应的第一特征值λ_(0,p)=inf{D_p(f):‖f‖_p=1,f非负且具有紧支撑}的上下界精细估计. 相似文献
5.
In order to obtain hitting time estimates for the asymmetric zero-range process (AZRP) on d, in dimensions d3, we characterize the principal eigenvalue of the generator of the AZRP with Dirichlet boundary on special domains. We obtain a Donsker-Varadhan variational representation and show that the corresponding eigenfunction is unique in a natural class of functions.Mathematics Subject Classification (2000):60K35, 82C22, 60J25 相似文献
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文献[1]利用基本Dirichlet型构造了基本可逆Q过程P*(t),本文在此基础上,利用马氏半群无穷小算子的谱分解理论和Q过程的DonsKer-Varahan熵得到P*(t)是不断的充要条件,并且还研究了P*(t)的不变函数和不变测度. 相似文献
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Harnack Inequalities for Jump Processes 总被引:11,自引:0,他引:11
We consider a class of pure jump Markov processes in R
d
whose jump kernels are comparable to those of symmetric stable processes. We establish a Harnack inequality for nonnegative functions that are harmonic with respect to these processes. We also establish regularity for the solutions to certain integral equations. 相似文献
9.
In 1995, Pacheco and Prabhu introduced the class of so-called Markov-additive processes of arrivals in order to provide a general class of arrival processes for queueing theory. In this paper, the above class is generalized considerably, including time-inhomogeneous arrival rates, general phase spaces and the arrival space being a general vector space (instead of the finite-dimensional Euclidean space). Furthermore, the class of Markov-additive jump processes introduced in the present paper is embedded into the existing theory of jump processes. The best known special case is the class of BMAP arrival processes. 相似文献
10.
Transition Probabilities for Symmetric Jump Processes 总被引:9,自引:0,他引:9
Richard F. Bass David A. Levin 《Transactions of the American Mathematical Society》2002,354(7):2933-2953
We consider symmetric Markov chains on the integer lattice in dimensions, where and the conductance between and is comparable to . We establish upper and lower bounds for the transition probabilities that are sharp up to constants.
11.
AbstractIn this paper, by the sub-super solution method we provide explicit lower bounds for the principal eigenvalue of the p-Laplacian on the unit ball. We compare our results with those of earlier studies and also demonstrate that they are in good agreement with numerical results. 相似文献
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Constructing some proper functional spaces, we obtain the corresponding norm for the operator (-.L)^-1, and then, via spectral theory, we revisit two variational formulas of the spectral gap, given by M. F. Chen [Front. Math. China, 2010, 5(3): 379-515], for transient birth-death processes. 相似文献
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本文给出树上两类非常返的生灭过程的第一Dirichlet特征值的变分公式.一类是配称测度有限时,给出以根为吸收点的Dirichlet特征值的变分公式;另一类是配称测度无限时,给出树上生灭过程的Dirichlet主特征值的变分公式. 相似文献
15.
We consider the Euler scheme for stochastic differential equations with jumps, whose intensity might be infinite and the jump structure may depend on the position. This general type of SDE is explicitly given for Feller processes and a general convergence condition is presented. In particular, the characteristic functions of the increments of the Euler scheme are calculated in terms of the symbol of the Feller process in a closed form. These increments are increments of Lévy processes and, thus, the Euler scheme can be used for simulation by applying standard techniques from Lévy processes. 相似文献
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WEI Na NIU Pengcheng LIU Haifeng 《偏微分方程(英文版)》2009,22(1):1-10
We prove some new Hardy type inequalities on the bounded domain with smooth boundary in the Carnot group. Several estimates of the first and second Dirich- let eigenvalues for the p-sub-Laplacian are established. 相似文献
17.
Bruno Schapira 《Probability Theory and Related Fields》2007,138(3-4):495-519
We introduce and study the natural counterpart of the Dunkl Markov processes in a negatively curved setting. We give a semimartingale
decomposition of the radial part, and some properties of the jumps. We prove also a law of large numbers, a central limit
theorem, and the convergence of the normalized process to the Dunkl process. Eventually we describe the asymptotic behavior
of the infinite loop as it was done by Anker, Bougerol and Jeulin in the symmetric spaces setting in (Iberoamericana 18: 41–97,
2002).
Partially supported by the European Commission (IHP Network HARP 2002–2006). 相似文献
18.
Patrick Guidotti 《Numerical Functional Analysis & Optimization》2013,34(5-6):507-531
In this paper, we address the problem of determining and efficiently computing an approximation to the eigenvalues of the negative Laplacian ? ? on a general domain Ω ? ?2 subject to homogeneous Dirichlet or Neumann boundary conditions. The basic idea is to look for eigenfunctions as the superposition of generalized eigenfunctions of the corresponding free space operator, in the spirit of the classical method of particular solutions (MPS). The main novelties of the proposed approach are the possibility of targeting each eigenvalue independently without the need for extensive scanning of the positive real axis and the use of small matrices. This is made possible by iterative inclusion of more basis functions in the expansions and a projection idea that transforms the minimization problem associated with MPS and its variants into a relatively simple zero-finding problem, even for expansions with very few basis functions. 相似文献
19.
We present a method to obtain lower bounds for firstDirichlet eigenvalue in terms of vector fields with positivedivergence. Applying this to the gradient of a distance functionwe obtain estimates of eigenvalue of balls inside the cut locus and of domains M B
N
(p, r) in submanifolds M
Nwith locally bounded mean curvature. Forsubmanifolds of Hadamard manifolds with bounded mean curvaturethese lower bounds depend only on the dimension of the submanifold and the bound on its mean curvature. 相似文献
20.
本文在狄氏型扰动的经典意义基础上,首次提出了狄氏型关于狄氏型的扰动的概念,并得到了若干使得扰动后的狄氏型具有拟正则性的条件,最后给出了一些应用。 相似文献