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Bisimulation for Labelled Markov Processes
 INFORMATION AND COMPUTATION
, 1997
"... In this paper we introduce a new class of labelled transition systems  Labelled Markov Processes  and define bisimulation for them. Labelled Markov processes are ..."
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Cited by 184 (25 self)
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In this paper we introduce a new class of labelled transition systems  Labelled Markov Processes  and define bisimulation for them. Labelled Markov processes are
A Model of Inductive Bias Learning
 Journal of Artificial Intelligence Research
, 2000
"... A major problem in machine learning is that of inductive bias: how to choose a learner's hypothesis space so that it is large enough to contain a solution to the problem being learnt, yet small enough to ensure reliable generalization from reasonablysized training sets. Typically such bias is ..."
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Cited by 174 (0 self)
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A major problem in machine learning is that of inductive bias: how to choose a learner's hypothesis space so that it is large enough to contain a solution to the problem being learnt, yet small enough to ensure reliable generalization from reasonablysized training sets. Typically such bias is supplied by hand through the skill and insights of experts. In this paper a model for automatically learning bias is investigated. The central assumption of the model is that the learner is embedded within an environment of related learning tasks. Within such an environment the learner can sample from multiple tasks, and hence it can search for a hypothesis space that contains good solutions to many of the problems in the environment. Under certain restrictions on the set of all hypothesis spaces available to the learner, we show that a hypothesis space that performs well on a sufficiently large number of training tasks will also perform well when learning novel tasks in the same environment. Exp...
SOME USEFUL FUNCTIONS FOR FUNCTIONAL LIMIT THEOREMS
, 1980
"... Many useful descriptions of stochastic models can be obtained from functional limit theorems (invariance principles or weak convergence theorems for probability meastires on function spaces). These descriptions typically come from standard functional limit theorems via the o^ntinuous mapping theorem ..."
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Cited by 76 (20 self)
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Many useful descriptions of stochastic models can be obtained from functional limit theorems (invariance principles or weak convergence theorems for probability meastires on function spaces). These descriptions typically come from standard functional limit theorems via the o^ntinuous mapping theorem. This paper facilitates applications of the continuous mapping theorem by determining when several important ftmctions and sequences of functions preserve convergence. The functions considered are composition, addition, composition plus addition, multiplication, supremtun, reflecting barrier, first passage time and time reversal. These functions provide means for proving new functional limit theorems from previous ones. These functions are useful, for example, to establish the stability or continuity of queues and other stochastic models.
Analysis and Geometry on Configuration Spaces
, 1997
"... In this paper foundations are presented to a new systematic approach to analysis and geometry for an important class of infinite dimensional manifolds, namely, configuration spaces. More precisely, a differential geometry is introduced on the configuration space \Gamma X over a Riemannian manifold X ..."
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Cited by 72 (10 self)
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In this paper foundations are presented to a new systematic approach to analysis and geometry for an important class of infinite dimensional manifolds, namely, configuration spaces. More precisely, a differential geometry is introduced on the configuration space \Gamma X over a Riemannian manifold X. This geometry is "nonflat" even if X = IR d . It is obtained as a natural lifting of the Riemannian structure on X. In particular, a corresponding gradient r \Gamma , divergence div \Gamma , and LaplaceBeltrami operator H \Gamma = \Gammadiv \Gamma r \Gamma are constructed. The associated volume elements, i.e., all measures ¯ on \Gamma X w.r.t. which r \Gamma and div \Gamma become dual operators on L 2 (\Gamma X ; ¯), are identified as exactly the mixed Poisson measures with mean measure equal to a multiple of the volume element dx on X. In particular, all these measures obey an integration by parts formula w.r.t. vector fields on \Gamma X . The corresponding Dirichlet...
SelfControl and the Theory of Consumption
, 1999
"... A model of temptation and selfcontrol for infinite horizon consumption problems under uncertainty is presented. A tractable class of preferences Dynamic selfcontrol (DSC) preferences is introduced. These preferences are recursive, separable, and describe agents who are tempted by immediate consu ..."
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Cited by 63 (3 self)
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A model of temptation and selfcontrol for infinite horizon consumption problems under uncertainty is presented. A tractable class of preferences Dynamic selfcontrol (DSC) preferences is introduced. These preferences are recursive, separable, and describe agents who are tempted by immediate consumption. The following implications of DSC behavior are established: Walrasian equilibrium exists in standard infinitehorizon economies with DSC preferences. Under suitable curvature conditions, in such equilibria, agents' steady state consumption is independent of their initial endowments. In a representative agent economy, increasing the agents preference for commitment while keeping selfcontrol constant increases the equity premium. Removing non binding constraints may change equilibrium allocations and prices. Debt contracts with DSC agents can be sustained even if the only feasible punishment for default is the termination of the contract.
Exponential Stability for Nonlinear Filtering
, 1996
"... We study the a.s. exponential stability of the optimal filter w.r.t. its initial conditions. A bound is provided on the exponential rate (equivalently, on the memory length of the filter) for a general setting both in discrete and in continuous time, in terms of Birkhoff's contraction coefficie ..."
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Cited by 58 (2 self)
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We study the a.s. exponential stability of the optimal filter w.r.t. its initial conditions. A bound is provided on the exponential rate (equivalently, on the memory length of the filter) for a general setting both in discrete and in continuous time, in terms of Birkhoff's contraction coefficient. Criteria for exponential stability and explicit bounds on the rate are given in the specific cases of a diffusion process on a compact manifold, and discrete time Markov chains on both continuous and discretecountable state spaces. R'esum'e Nous 'etudions la stabilit'e du filtre optimal par raport `a ses conditions initiales. Le taux de d'ecroissance exponentielle est calcul'e dans un cadre g'en'eral, pour temps discret et temps continu, en terme du coefficient de contraction de Birkhoff. Des crit`eres de stabilit'e exponentielle et des bornes explicites sur le taux sont calcul'ees pour les cas particuliers d'une diffusion sur une vari'ete compacte, ainsi que pour des chaines de Markov sur ...
Martingale proofs of manyserver heavytraffic limits for Markovian queues
 PROBABILITY SURVEYS
, 2007
"... ..."
Metrics for Labelled Markov Systems
, 2001
"... The notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions. Thus, a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent. This instability is due to the quantitative nature of ..."
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Cited by 47 (10 self)
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The notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions. Thus, a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent. This instability is due to the quantitative nature of probabilistic processes. In a situation where the process behaviour has a quantitative aspect there should be a more robust approach to process equivalence. This paper studies a metric between labelled Markov processes. This metric has the property that processes are at zero distance if and only if they are bisimilar. The metric is inspired by earlier work on logics for characterizing bisimulation and is related, in spirit, to the Hutchinson metric.
Laws of Large Numbers for Dynamical Systems with Randomly Matched Individuals
 Journal of Economic Theory
, 1992
"... Biologists and economists have analyzed populations where each individual interacts with randomly selected individuals. The random matching generates a very complicated stochastic system. Consequently biologists and economists have approximated such a system with a deterministic system. The justitic ..."
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Cited by 44 (0 self)
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Biologists and economists have analyzed populations where each individual interacts with randomly selected individuals. The random matching generates a very complicated stochastic system. Consequently biologists and economists have approximated such a system with a deterministic system. The justitication for such an approximation is that the population is assumed to be very large and thus some law of large numbers must hold. This paper gives a characterization of random matching schemes for countably infinite populations. In particular this paper shows that there exists a random matching scheme such that the stochastic system and the deterministic system are the same. Journal of Economic Literature Classification