共查询到20条相似文献,搜索用时 11 毫秒
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The isomorphism theorem of Dynkin is definitely an important tool to investigate the problems raised in terms of local times of Markov processes. This theorem concerns continuous time Markov processes. We give here an equivalent version for Markov chains. 相似文献
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Summary A general class of statistics based on sequential ranks is introduced. Under suitable regularity conditions, an almost sure representation and invariance principle are established for this class. In particular, it is shown that these statistics can obey invariance principles that are radically different from those obeyed by the usual full rank statistics.Research supported by the CSIR and the University of South AfricaResearch supported by the University of Delaware Research Foundation, Grant #8325530015 相似文献
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Limit theorems for branching Markov processes 总被引:1,自引:0,他引:1
We establish almost sure limit theorems for a branching symmetric Hunt process in terms of the principal eigenvalue and the ground state of an associated Schrödinger operator. Here the branching rate and the branching mechanism can be state-dependent. In particular, the branching rate can be a measure belonging to a certain Kato class and is allowed to be singular with respect to the symmetrizing measure for the underlying Hunt process X. The almost sure limit theorems are established under the assumption that the associated Schrödinger operator of X has a spectral gap. Such an assumption is satisfied if the underlying process X is a Brownian motion, a symmetric α-stable-like process on or a relativistic symmetric stable process on . 相似文献
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Douglas P. Kennedy 《Stochastic Processes and their Applications》1973,1(3):269-278
Limit distributions are given for both the dam content at time n and the limiting dam content in the nth dam, as n tends to infinity, for a sequence of finite dams in discrete time, under assumptions which correspond to the various cases of heavy traffic in queueing theory. The proof employed is an application of the theory of weak convergence of probability measures. 相似文献
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设{Xn,n≥0}是一列非齐次马尔科夫链,{an,n≥0}是一列固定的非负整数序列.首先构造了一个带参数的广义似然比函数,然后利用Borel-Cantelli引理证明随机变量序列几乎处处收敛性,得到了关于可列非齐次马氏链序偶广义平均的若干极限定理,推广了已有的结果. 相似文献
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S. Horowitz 《Israel Journal of Mathematics》1969,7(1):60-62
A necessary and sufficient condition for convergence of Markov processesL
∞ is given. As a consequence we get a theorem concerning the convergence of Harris processes.
This paper is a part of the author’s Ph.D. thesis to be submitted to the Hebrew University of Jerusalem. The author wishes
to express his thanks to Professor S. R. Foguel for much valuable advice and encouragement. 相似文献
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This paper develops bounds on the rate of decay of powers of Markov kernels on finite state spaces. These are combined with eigenvalue estimates to give good bounds on the rate of convergence to stationarity for finite Markov chains whose underlying graph has moderate volume growth. Roughly, for such chains, order (diameter) steps are necessary and suffice to reach stationarity. We consider local Poincaré inequalities and use them to prove Nash inequalities. These are bounds onl
2-norms in terms of Dirichlet forms andl
1-norms which yield decay rates for iterates of the kernel. This method is adapted from arguments developed by a number of authors in the context of partial differential equations and, later, in the study of random walks on infinite graphs. The main results do not require reversibility. 相似文献
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Thomas G. Kurtz 《Stochastic Processes and their Applications》1978,6(3):223-240
A variety of continuous parameter Markov chains arising in applied probability (e.g. epidemic and chemical reaction models) can be obtained as solutions of equations of the form where , the Y1 are independent Poisson processes, and N is a parameter with a natural interpretation (e.g. total population size or volume of a reacting solution).The corresponding deterministic model, satisfies Under very general conditions limN→∞XN(t)=X(t) a.s. The process XN(t) is compared to the diffusion processes given by and Under conditions satisfied by most of the applied probability models, it is shown that XN,ZN and V can be constructed on the same sample space in such a way that and 相似文献
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Shlomo Levental 《Probability Theory and Related Fields》1988,80(1):101-118
Summary We study uniform limit theorems for regenerative processes and get strong law of large numbers and central limit theorem of this type. Then we apply those results to Harris recurrent Markov chains based on some ideas of K. Athreya, P. Ney and E. Nummelin. 相似文献
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Dr. Krishna Balasundaram Athreya 《Probability Theory and Related Fields》1969,12(4):320-332
Summary Let X(t)=(X
1
(t), X
2
(t), , X
t
(t)) be a k-type (2k<) continuous time, supercritical, nonsingular, positively regular Markov branching process. Let M(t)=((m
ij
(t))) be the mean matrix where m
ij
(t)=E(X
j
(t)¦X
r
(0)=
ir
for r=1, 2, , k) and write M(t)=exp(At). Let be an eigenvector of A corresponding to an eigenvalue . Assuming second moments this paper studies the limit behavior as t of the stochastic process
. It is shown that i) if 2 Re >1, then · X(t)e{–t¦ converges a.s. and in mean square to a random variable. ii) if 2 Re 1 then [ · X(t)] f(v · X(t)) converges in law to a normal distribution where f(x)=(x)
–1
if 2 Re <1 and f(x)=(x log x)–1 if 2 Re =1, 1 the largest real eigenvalue of A and v the corresponding right eigenvector.Research supported in part under contracts N0014-67-A-0112-0015 and NIH USPHS 10452 at Stanford University. 相似文献
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N. I. Chernov 《Probability Theory and Related Fields》1995,101(3):321-362
Summary We prove the central limit theorem and weak invariance principle for abstract dynamical systems based on bounds on their mixing coefficients. We also develop techniques of Markov approximations for dynamical systems. We apply our results to expanding interval maps, Axiom A diffeomorphisms, chaotic billiards and hyperbolic attractors. 相似文献
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Sangita Kulathinal Lagnojita Ghosh 《International Journal of Mathematical Education in Science & Technology》2013,44(4):498-502
In an undergraduate course on stochastic processes, Markov chains are discussed in great detail. Textbooks on stochastic processes provide interesting properties of finite Markov chains. This note discusses one such property regarding the number of steps in which a state is reachable or accessible from another state in a finite Markov chain with M (≥ 2) states. 相似文献
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Two kinds of eigentime identity for asymmetric finite Markov chains are proved both in the ergodic case and the transient
case. 相似文献