Using linear programming in Petri net analysis
Solving a class of multivariate integration problems via Laplace techniques
We consider the problem of calculating a closed form expression for the integral of a real-valued function f:ℝⁿ → ℝ on a set S. We specialize to the particular cases when S is a convex polyhedron or an ellipsoid, and the function f is either a generalized polynomial, an exponential of a linear form (including trigonometric polynomials) or an exponential of a quadratic form. Laplace transform techniques allow us to obtain either a closed form expression, or a series representation that can be handled...
On the probabilistic multichain Poisson equation
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.
Quasi-Feller Markov chains.
Homogeneous functions and conjugacy.
On the setwise convergence of sequences of measures.
Fatou's lemma and Lebesgue's convergence theorem for measures.
Invariant probabilities for Feller-Markov chains.
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