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Seminario: Stochastic equations for processes built from bounded generators

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Stochastic equations for processes built from bounded generators  

Giovedi' 11 maggio 2017 alle ore 16.00, presso l'aula seminari della sede di viale della Pineta 4 del Dipartimento di Economia, il

Prof. T. G. Kurtz, della University of Wisconsin-Madison,

terrà un seminario dal titolo:

"Stochastic equations for processes built from bounded generators"

The generator for a pure jump process with bounded jump rate is a  bounded operator on the space of measurable functions.  For any such  process, it is simple to write a stochastic equation driven by a  Poisson random measure.  Uniqueness for both the stochastic equation  and the corresponding martingale problem is immediate, and  consequently, the martingale problem and the stochastic equation are  equivalent in the sense that they uniquely characterize the same  process.  A variety of Markov processes, including many interacting  particle models, have generators which are at least formally given  by infinite sums of bounded generators.  In considerable generality,  we can write stochastic equations that are equivalent to these  generators in the sense that every solution of the stochastic  equation is a solution of the martingale problem and every solution  of the martingale problem determines a weak solution of the  stochastic equation.  It follows that uniqueness for one approach is  equivalent to uniqueness for the other.