Electronic Journal of Probability
- Electron. J. Probab.
- Volume 14 (2009), paper no. 73, 2130-2155.
A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Methods
We present a functional central limit theorem for a new class of interacting Markov chain Monte Carlo algorithms. These stochastic algorithms have been recently introduced to solve non-linear measure-valued equations. We provide an original theoretical analysis based on semigroup techniques on distribution spaces and fluctuation theorems for self-interacting random fields. Additionally we also present a series of sharp mean error bounds in terms of the semigroup associated with the first order expansion of the limiting measure-valued process. We illustrate our results in the context of Feynman-Kac semigroups
Electron. J. Probab., Volume 14 (2009), paper no. 73, 2130-2155.
Accepted: 4 October 2009
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F05: Central limit and other weak theorems
Secondary: 60J05: Discrete-time Markov processes on general state spaces 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40] 68U20: Simulation [See also 65Cxx] 80M31: Monte Carlo methods
This work is licensed under aCreative Commons Attribution 3.0 License.
Bercu, Bernard; Del Moral, Pierre; Doucet, Arnaud. A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Methods. Electron. J. Probab. 14 (2009), paper no. 73, 2130--2155. doi:10.1214/EJP.v14-701. https://projecteuclid.org/euclid.ejp/1464819534