A two-disorder detection problem

Krzysztof Szajowski

Displaying similar documents to “A two-disorder detection problem”

Optimal stopping of a risk process

Elżbieta Ferenstein, Andrzej Sierociński (1997)

Applicationes Mathematicae

Similarity:

Optimal stopping time problems for a risk process $U_{t} = u + c t - \sum_{n = 0}^{N (t)} X_{n}$ where the number N(t) of losses up to time t is a general renewal process and the sequence of $X_{i}$ ’s represents successive losses are studied. N(t) and $X_{i}$ ’s are independent. Our goal is to maximize the expected return before the ruin time. The main results are closely related to those obtained by Boshuizen and Gouweleew [2].

Stability estimating in optimal sequential hypotheses testing

Evgueni I. Gordienko, Andrey Novikov, Elena Zaitseva (2009)

Kybernetika

Similarity:

We study the stability of the classical optimal sequential probability ratio test based on independent identically distributed observations $X_{1}, X_{2}, \dots$ when testing two simple hypotheses about their common density $f$ : $f = f_{0}$ versus $f = f_{1}$ . As a functional to be minimized, it is used a weighted sum of the average (under $f_{0}$ ) sample number and the two types error probabilities. We prove that the problem is reduced to stopping time optimization for a ratio process generated by $X_{1}, X_{2}, \dots$ with the density $f_{0}$ . For $τ_{*}$ being...

Transformation of Markov processes by multiplicative functionals

K. Ito, S. Watanabe (1965)

Annales de l'institut Fourier

Similarity:

Il s’agit du développement détaillé de l’idée que l’un des auteurs, K. Itô, a présentée au Colloque de théorie du potentiel. Étant donné une fonctionnelle multiplicative $α$ , d’un processus de Hunt $X_{t}$ , on construit le $α$ -sous processus de $X_{t}$ . La section 1 donne un aperçu historique et une idée sommaire de la construction. La section 2 est consacrée au théorème de factorisation pour super martingale positive, d’après quoi on prouve qu’une fonctionnelle multiplicative super régulière...

Sample-path average cost optimality for semi-Markov control processes on Borel spaces: unbounded costs and mean holding times

Oscar Vega-Amaya, Fernando Luque-Vásquez (2000)

Applicationes Mathematicae

Similarity:

We deal with semi-Markov control processes (SMCPs) on Borel spaces with unbounded cost and mean holding time. Under suitable growth conditions on the cost function and the mean holding time, together with stability properties of the embedded Markov chains, we show the equivalence of several average cost criteria as well as the existence of stationary optimal policies with respect to each of these criteria.

Sample path average optimality of Markov control processes with strictly unbounded cost

Oscar Vega-Amaya (1999)

Applicationes Mathematicae

Similarity:

We study the existence of sample path average cost (SPAC-) optimal policies for Markov control processes on Borel spaces with strictly unbounded costs, i.e., costs that grow without bound on the complement of compact subsets. Assuming only that the cost function is lower semicontinuous and that the transition law is weakly continuous, we show the existence of a relaxed policy with 'minimal' expected average cost and that the optimal average cost is the limit of discounted programs. Moreover,...

Limiting average cost control problems in a class of discrete-time stochastic systems

Nadine Hilgert, Onesimo Hernández-Lerma (2001)

Applicationes Mathematicae

Similarity:

We consider a class of $ℝ^{d}$ -valued stochastic control systems, with possibly unbounded costs. The systems evolve according to a discrete-time equation $x_{t + 1} = G ₙ (x_{t}, a_{t}) + ξ_{t}$ (t = 0,1,... ), for each fixed n = 0,1,..., where the $ξ_{t}$ are i.i.d. random vectors, and the Gₙ are given functions converging pointwise to some function $G_{\infty}$ as n → ∞. Under suitable hypotheses, our main results state the existence of stationary control policies that are expected average cost (EAC) optimal and sample path average cost (SPAC)...

Optimal stopping for Markov Processes

Massimo Lorenzani (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

In questa nota presentiamo dei nuovi risultati sul problema di tempo d’arresto ottimale per processi di Markov con tempo discreto.

Concentration of measure on product spaces with applications to Markov processes

Gordon Blower, François Bolley (2006)

Studia Mathematica

Similarity:

For a stochastic process with state space some Polish space, this paper gives sufficient conditions on the initial and conditional distributions for the joint law to satisfy Gaussian concentration inequalities and transportation inequalities. In the case of the Euclidean space $ℝ^{m}$ , there are sufficient conditions for the joint law to satisfy a logarithmic Sobolev inequality. In several cases, the constants obtained are of optimal order of growth with respect to the number of random variables,...

On the optimal setting of the $h p$ -version of the finite element method

Chleboun, Jan

Similarity:

The goal of this contribution is to find the optimal finite element space for solving a particular boundary value problem in one spatial dimension. In other words, the optimal use of available degrees of freedom is sought after. This is done through optimizing both the mesh and the polynomial degree of the basis functions. The resulting combinatorial optimization problem is solved in parallel by a Matlab program running on a cluster of multi-core personal computers.