2012/02/13 by Amaury Lambert, Lambert, Amaury, Florian Simatos +1
Economics, Econometrics and Finance · Mathematics · #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.48550/arxiv.1202.2878
Final version accepted for publication in Annales de l'Institut Henri Poincaré
arxiv created 2013/05/23 · arxiv updated 2013/05/24
We consider regenerative processes with values in some Polish space. We define their ε-big excursions as excursions e such that f(e)>ε, where f is some given functional on the space of excursions which can be thought of as, e.g., the length or the height of e. We establish a general condition that guarantees the convergence of a sequence of regenerative processes involving the convergence of ε-big excursions and of their endpoints, for all εin a countable set whose closure contains 0. Finally, we provide various sufficient conditions on the excursion measures of this sequence for this general condition to hold and discuss possible generalizations of our approach to processes that can be written as the concatenation of i.i.d. paths.