Displaying similar documents to “On additive and multiplicative (controlled) Poisson equations”

On the probabilistic multichain Poisson equation

Onésimo Hernández-Lerma, Jean B. Lasserre (2001)

Applicationes Mathematicae

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This paper introduces necessary and/or sufficient conditions for the existence of solutions (g,h) to the probabilistic multichain Poisson equation (a) g = Pg and (b) g+h-Ph = f, with a given charge f, where P is a Markov kernel (or transition probability function) on a general measurable space. The existence conditions are derived via three different approaches, using (1) canonical pairs, (2) Cesàro averages, and (3) resolvents.

Piecewise-deterministic Markov processes

Jolanta Kazak (2013)

Annales Polonici Mathematici

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Poisson driven stochastic differential equations on a separable Banach space are examined. Some sufficient conditions are given for the asymptotic stability of a Markov operator P corresponding to the change of distribution from jump to jump. We also give criteria for the continuous dependence of the invariant measure for P on the intensity of the Poisson process.

The risk-sensitive Poisson equation for a communicating Markov chain on a denumerable state space

Rolando Cavazos-Cadena (2009)

Kybernetika

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This work concerns a discrete-time Markov chain with time-invariant transition mechanism and denumerable state space, which is endowed with a nonnegative cost function with finite support. The performance of the chain is measured by the (long-run) risk-sensitive average cost and, assuming that the state space is communicating, the existence of a solution to the risk-sensitive Poisson equation is established, a result that holds even for transient chains. Also, a sufficient criterion...

Quantization of pencils with a gl-type Poisson center and braided geometry

Dimitri Gurevich, Pavel Saponov (2011)

Banach Center Publications

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We consider Poisson pencils, each generated by a linear Poisson-Lie bracket and a quadratic Poisson bracket corresponding to a so-called Reflection Equation Algebra. We show that any bracket from such a Poisson pencil (and consequently, the whole pencil) can be restricted to any generic leaf of the Poisson-Lie bracket. We realize a quantization of these Poisson pencils (restricted or not) in the framework of braided affine geometry. Also, we introduce super-analogs of all these Poisson...

Asymptotic evaluation of the Poisson measures for tubes around jump curves

Xavier Bardina, Carles Rovira, Samy Tindel (2002)

Applicationes Mathematicae

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We find the asymptotic behavior of P(||X-ϕ|| ≤ ε) when X is the solution of a linear stochastic differential equation driven by a Poisson process and ϕ the solution of a linear differential equation driven by a pure jump function.

Compound Compound Poisson Risk Model

Minkova, Leda D. (2009)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 60K10, 62P05. The compound Poisson risk models are widely used in practice. In this paper the counting process in the insurance risk model is a compound Poisson process. The model is called Compound Compound Poisson Risk Model. Some basic properties and ruin probability are given. We analyze the model under the proportional reinsurance. The optimal retention level and the corresponding adjustment coefficient are obtained. The particular...