共查询到20条相似文献,搜索用时 15 毫秒
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Measure-free discrete time stochastic processes in Riesz spaces were formulated and studied by Kuo, Labuschagne and Watson. Aspects relating martingales, stopping times, convergence of these processes as well as various decomposition were considered. Here we formulate and study Markov processes in a measure-free Riesz space setting. 相似文献
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We study controlled Markov processes where multiple decisions need to be made for each state. We present conditions on the cost structure and the state transition mechanism of the process under which optimal decisions are restricted to a subset of the decision space. As a result, the numerical computation of the optimal policy may be significantly expedited. 相似文献
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Andrey A. Dorogovtsev 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(5):395-407
We consider measure-valued processes with constant mass in Hilbert space. The stochastic flow which carries the mass satisfies a stochastic differential equation with coefficients depending on the mass distribution. This mass distribution can be considered as the conditional distribution of the solution of a certain SDE. In contrast to the filtration equation, in our case the random measure cannot diffuse: a single particle cannot break up or turn into clouds. The Markov structure of the measure-valued processes obtained is studied and a comparison with Fleming–Viot processes is presented. 相似文献
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C. T. Shih 《Probability Theory and Related Fields》1994,98(2):185-207
Summary LetE be a noncompact locally compact second countable Hausdorff space. We consider the question when, given a family of finite nonzero measures onE that behave like harmonic measures associated with all relatively compact open sets inE (i.e. that satisfy a certain consistency condition), one can construct a Markov process onE and a multiplicative functional with values in [0, ) such that the hitting distributions of the process inflated by the multiplicative functional yield the given harmonic measures. We achieve this construction under weak continuity and local transience conditions on these measures that are natural in the theory of Markov processes, and a mild growth restriction on them. In particular, if the spaceE equipped with the measures satisfies the conditions of a harmonic space, such a Markov process and associated multiplicative functional exist. The result extends in a new direction the work of many authors, in probability and in axiomatic potential theory, on constructing Markov processes from given hitting distributions (i.e. from harmonic measures that have total mass no more than 1). 相似文献
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Consider two transient Markov processes (Xvt)tεR·, (Xμt)tεR· with the same transition semigroup and initial distributions v and μ. The probability spaces supporting the processes each are also assumed to support an exponentially distributed random variable independent of the process.
We show that there exist (randomized) stopping times S for (Xvt), T for (Xμt) with common final distribution, L(XvS|S < ∞) = L(XμT|T < ∞), and the property that for t < S, resp. t < T, the processes move in disjoint portions of the state space. For such a coupling (S, T) it is shown
where denotes the bounded harmonic functions of the Markov transition semigroup. Extensions, consequences and applications of this result are discussed. 相似文献
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E.B Dynkin 《Journal of Functional Analysis》1982,47(3):381-418
This is the second paper in a series devoted to Green's and Dirichlet spaces. In the first paper, we have investigated Green's space and the Dirichlet space associated with a symmetric Markov transition function pt(x, B). Now we assume that p is a transition function of a fine Markov process X and we prove that: (a) the space can be built from functions which are right continuous along almost all paths; (b) the positive cone + in can be identified with a cone M of measures on the state space; (c) the positive cone + in can be interpreted as the cone of Green's potentials of measures μ?M. To every measurable set B in the state space E there correspond a subspace (B) of and a subspace (B) of . The orthogonal projections of onto and of onto (B) can be expressed in terms of the hitting probabilities of B by the Markov process X. As the main tool, we use additive functionals of X corresponding to measures μ?M. 相似文献
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Torbjörn Kolsrud 《Journal of Theoretical Probability》1989,2(4):399-418
We derive explicit isomorphism formulas between weighted Dirichlet integrals for harmonic functions and boundary Dirichlet forms. Applications yield results on traces of Markov processes and convergence quasieverywhere of harmonic functions. 相似文献
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J. Heber 《Geometric And Functional Analysis》2006,16(4):869-890
We classify noncompact homogeneous spaces which are Einstein and asymptotically harmonic. This completes the classification of Riemannian harmonic spaces in the homogeneous case: Any simply connected homogeneous harmonic space is flat, or rank-one symmetric, or a nonsymmetric
Damek–Ricci space. Independently, Y. Nikolayevsky has obtained the latter classification under the additional assumption of
nonpositive sectional curvatures [N2].
Supported in part by DFG priority program “Global Differential Geometry” (SPP 1154).
Received: September 2004; Revision: June 2005; Accepted: September 2005 相似文献
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Quanxin Zhu 《Mathematical Methods of Operations Research》2007,66(2):299-313
In this paper, we study the average optimality for continuous-time controlled jump Markov processes in general state and action spaces. The criterion to be minimized is the average expected costs. Both the transition rates and the cost rates are allowed to be unbounded. We propose another set of conditions under which we first establish one average optimality inequality by using the well-known “vanishing discounting factor approach”. Then, when the cost (or reward)
rates are nonnegative (or nonpositive), from the average optimality inequality we prove the existence of an average optimal
stationary policy in all randomized history dependent policies by using the Dynkin formula and the Tauberian theorem. Finally, when the cost (or reward) rates have neither upper nor lower bounds, we also prove the existence of an average optimal policy in all (deterministic) stationary policies by constructing a “new”
cost (or reward) rate.
Research partially supported by the Natural Science Foundation of China (Grant No: 10626021) and the Natural Science Foundation
of Guangdong Province (Grant No: 06300957). 相似文献
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Quan-xin Zhu 《应用数学学报(英文版)》2011,27(4):613-624
In this paper we study the average sample-path cost(ASPC) problem for continuous-time Markov decision processes in Polish spaces.To the best of our knowledge,this paper is a first attempt to study the ASPC criterion on continuous-time MDPs with Polish state and action spaces.The corresponding transition rates are allowed to be unbounded,and the cost rates may have neither upper nor lower bounds.Under some mild hypotheses,we prove the existence of ε(ε≥ 0)-ASPC optimal stationary policies based on two differe... 相似文献
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Onésimo Hernández-Lerma Juan González-Hernández 《Mathematical Methods of Operations Research》2000,52(2):271-285
We consider constrained discounted-cost Markov control processes in Borel spaces, with unbounded costs. Conditions are given
for the constrained problem to be solvable, and also equivalent to an equality-constrained (EC) linear program. In addition, it is shown that there is no duality gap between EC and its dual program EC*, and that, under additional assumptions, also EC* is solvable, so that in fact the strong duality condition holds. Finally, a Farkas-like theorem is included, which gives necessary and sufficient conditions for the primal program
EC to be consistent. 相似文献
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This paper deals with discrete-time Markov control processes withBorel state and control spaces, with possiblyunbounded costs andnoncompact control constraint sets, and the average cost criterion. Conditions are given for the convergence of the value iteration algorithm to the optimal average cost, and for a sequence of finite-horizon optimal policies to have an accumulation point which is average cost optimal.This research was partially supported by the Consejo Nacional de Ciencia y Tecnología (CONACyT) under grant 1332-E9206. 相似文献
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Recently Korevaar and Schoen developed a Sobolev theory for maps from smooth (at least ) manifolds into general metric spaces by proving that the weak limit of appropriate average difference quotients is well
behaved. Here we extend this theory to functions defined over Lipschitz manifold. As an application we then prove an existence
theorem for harmonic maps from Lipschitz manifolds to NPC metric spaces.
Received December 6, 1996 / Accepted March 4, 1997 相似文献
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We prove that a Riemannian manifold is harmonic if and only if there exists a divergence-preserving geodesic transformation
with respect to each point which is not volume-preserving. 相似文献
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