%0 Journal Article %1 pages2018first %A Pagès, Gilles %A Rey, Clément %D 2018 %K stochastic-algorithm %T First and second order Central Limit Theorems for the recursive computation of the invariant distribution of a Feller process %U http://arxiv.org/abs/1801.05710 %X This paper studies the convergence of empirical measures of a stochastic approximation toward the invariant distribution of a Feller process. In particular, we provide a general and abstract approach to establish Central Limit Theorems (CLT) with given rate . Moreover, considering weighted empirical measures of a weak order two stochastic approximation, we show its second order convergence while the CLT for standard empirical measures has order one. We also propose various applications: First order CLT for the approximation of Markov Brownian diffusion stationary regimes with Euler scheme (where we recover existing results from literature) and second order CLT for the approximation of Brownian diffusion stationary regimes using Talay scheme (1990) of weak order two.

@article{pages2018first, abstract = {This paper studies the convergence of empirical measures of a stochastic approximation toward the invariant distribution of a Feller process. In particular, we provide a general and abstract approach to establish Central Limit Theorems (CLT) with given rate . Moreover, considering weighted empirical measures of a weak order two stochastic approximation, we show its second order convergence while the CLT for standard empirical measures has order one. We also propose various applications: First order CLT for the approximation of Markov Brownian diffusion stationary regimes with Euler scheme (where we recover existing results from literature) and second order CLT for the approximation of Brownian diffusion stationary regimes using Talay scheme (1990) of weak order two.}, added-at = {2018-01-18T18:57:53.000+0100}, author = {Pagès, Gilles and Rey, Clément}, biburl = {https://www.bibsonomy.org/bibtex/25091b96a07ce6b284640abb8bb1867d0/claired}, description = {First and second order Central Limit Theorems for the recursive computation of the invariant distribution of a Feller process}, interhash = {7a3e5c4ac2da872ca1228bd580693e52}, intrahash = {5091b96a07ce6b284640abb8bb1867d0}, keywords = {stochastic-algorithm}, note = {cite arxiv:1801.05710Comment: arXiv admin note: substantial text overlap with arXiv:1703.04557, arXiv:1712.04044}, timestamp = {2018-01-18T18:57:53.000+0100}, title = {First and second order Central Limit Theorems for the recursive computation of the invariant distribution of a Feller process}, url = {http://arxiv.org/abs/1801.05710}, year = 2018 }