Convergence in law for certain additive functionals of symmetric stable processes under strong topology

Pr¨ unster [8] an extension of the L´evy process formula to integral functionals up to t = ∞ of increasing additive processes is discussed, and their formula (7) can be seen as

Conversely, it still remains an open problem for instance to find the value of the persistence exponent for the integrated fractional Brownian motion, or for the twice

In the second part of the paper, we develop a similar analysis for functionals of two indepen- dent fractional Brownian motions (or, more generally, Volterra processes) related to

Abstract We obtain a local limit theorem for the laws of a class of Brownian additive func- tionals and we apply this result to a penalisation problem... This is the content of

A o-algebra of well-measurable sets is associated with any right filtration M^ This is the o-algebra on T X Q gene- rated by all the evanescent functions and by all the right

Additive functionals, Markov chains, Renewal processes, Partial sums, Harris recurrent, Strong mixing, Absolute regularity, Geometric ergodicity, Invariance principle,

chains., Ann. Nagaev, Some limit theorems for stationary Markov chains, Teor. Veretennikov, On the Poisson equation and diffusion approximation. Rebolledo, Central limit theorem

It has not been possible to translate all results obtained by Chen to our case since in contrary to the discrete time case, the ξ n are no longer independent (in the case of