A. A. Markov, ses probabilités en chaîne et les statistiques linguistiques
A central limit theorem for two-dimensional random walks in a cone
We prove that a planar random walk with bounded increments and mean zero which is conditioned to stay in a cone converges weakly to the corresponding Brownian meander if and only if the tail distribution of the exit time from the cone is regularly varying. This condition is satisfied in many natural examples.
A connection between controlled Markov chains and martingales
A criterion of asymptotic stability for Markov-Feller e-chains on Polish spaces
Stettner [Bull. Polish Acad. Sci. Math. 42 (1994)] considered the asymptotic stability of Markov-Feller chains, provided the sequence of transition probabilities of the chain converges to an invariant probability measure in the weak sense and converges uniformly with respect to the initial state variable on compact sets. We extend those results to the setting of Polish spaces and relax the original assumptions. Finally, we present a class of Markov-Feller chains with a linear state space model which...
A dozen de Finetti-style results in search of a theory
A game model referring to the control of independent discrete time stochastic processes
A Gauss-Kuzmin theorem for the Rosen fractions
Using the natural extensions for the Rosen maps, we give an infinite-order-chain representation of the sequence of the incomplete quotients of the Rosen fractions. Together with the ergodic behaviour of a certain homogeneous random system with complete connections, this allows us to solve a variant of Gauss-Kuzmin problem for the above fraction expansion.
A generalization of Straube's theorem: existence of absolutely continuous invariant measures for random maps.
A generalization of Ueno's inequality for n-step transition probabilities
We provide a generalization of Ueno's inequality for n-step transition probabilities of Markov chains in a general state space. Our result is relevant to the study of adaptive control problems and approximation problems in the theory of discrete-time Markov decision processes and stochastic games.
A Markov process underlying the generalized Syracuse algorithm
A note on the characterization ofsome minification processes
We present a stochastic model which yields a stationary Markov process whose invariant distribution is maximum stable with respect to the geometrically distributed sample size. In particular, we obtain the autoregressive Pareto processes and the autoregressive logistic processes introduced earlier by Yeh et al
A probablistic origin for a new class of bivariate polynomials.
A quenched weak invariance principle
In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and nonirreducible Markov chains are given. The proofs are based on the normal approximation of double indexed martingale-like sequences, an approach which has interest in itself.
A regeneration proof of the central limit theorem for uniformly ergodic Markov chains.
A simple proof of a theorem on Markov operators
A stochastic scheme of approximation for ordinary differential equations.
A vanishing discount limit theorem for controlled Markov chains
A weak quasi-Lindelöf property and quasi-fine supports of measures.
Adaptive control for discrete-time Markov processes with unbounded costs: Discounted criterion
We study the adaptive control problem for discrete-time Markov control processes with Borel state and action spaces and possibly unbounded one-stage costs. The processes are given by recurrent equations with i.i.d. -valued random vectors whose density is unknown. Assuming observability of we propose the procedure of statistical estimation of that allows us to prove discounted asymptotic optimality of two types of adaptive policies used early for the processes with bounded costs.
Algorithmical Definition of Finite Markov Sequence