Displaying similar documents to “Markov dilation of diffusion type processes and its application to the financial mathematics.”

On the core property of the cylinder functions class in the construction of interacting particle systems

Anja Voss-Böhme (2011)

Kybernetika

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For general interacting particle systems in the sense of Liggett, it is proven that the class of cylinder functions forms a core for the associated Markov generator. It is argued that this result cannot be concluded by straightforwardly generalizing the standard proof technique that is applied when constructing interacting particle systems from their Markov pregenerators.

Average cost Markov control processes with weighted norms: value iteration

Evgueni Gordienko, Onésimo Hernández-Lerma (1995)

Applicationes Mathematicae

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This paper shows the convergence of the value iteration (or successive approximations) algorithm for average cost (AC) Markov control processes on Borel spaces, with possibly unbounded cost, under appropriate hypotheses on weighted norms for the cost function and the transition law. It is also shown that the aforementioned convergence implies strong forms of AC-optimality and the existence of forecast horizons.

The first exit of almost strongly recurrent semi-Markov processes

Joachim Domsta, Franciszek Grabski (1995)

Applicationes Mathematicae

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Let ( · ) , n ∈ N, be a sequence of homogeneous semi-Markov processes (HSMP) on a countable set K, all with the same initial p.d. concentrated on a non-empty proper subset J. The subrenewal kernels which are restrictions of the corresponding renewal kernels on K×K to J×J are assumed to be suitably convergent to a renewal kernel P (on J×J). The HSMP on J corresponding to P is assumed to be strongly recurrent. Let [ π j ; j ∈ J] be the stationary p.d. of the embedded Markov chain. In terms of...

Strangely sweeping one-dimensional diffusion

Ryszard Rudnicki (1993)

Annales Polonici Mathematici

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Let X(t) be a diffusion process satisfying the stochastic differential equation dX(t) = a(X(t))dW(t) + b(X(t))dt. We analyse the asymptotic behaviour of p(t) = ProbX(t) ≥ 0 as t → ∞ and construct an equation such that l i m s u p t → ∞ t - 1 ∫ 0 t p ( s ) d s = 1 and l i m i n f t → ∞ t - 1 ∫ 0 t p ( s ) d s = 0 .