Displaying similar documents to “An essay on the general theory of stochastic processes.”

Functionals of spatial point processes having a density with respect to the Poisson process

Viktor Beneš, Markéta Zikmundová (2014)

Kybernetika

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U -statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Itô chaos expansion. In the second half we obtain more explicit results for a system of U -statistics of some parametric models in stochastic geometry. In the logarithmic form functionals are connected to Gibbs models. There is an inequality...

Strong average optimality criterion for continuous-time Markov decision processes

Qingda Wei, Xian Chen (2014)

Kybernetika

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This paper deals with continuous-time Markov decision processes with the unbounded transition rates under the strong average cost criterion. The state and action spaces are Borel spaces, and the costs are allowed to be unbounded from above and from below. Under mild conditions, we first prove that the finite-horizon optimal value function is a solution to the optimality equation for the case of uncountable state spaces and unbounded transition rates, and that there exists an optimal...