Stochastic Analysis and Optimal Scaling

Specialeforsvar ved Jonas Rysgaard Jensen

Titel: Stochastic Analysis and Optimal Scaling

  

Abstract: In this thesis we study two different approaches to establishing weak convergence of stochastic processes in continuous time and the application of these approaches to the optimal scaling problem. In the first part of the thesis, we review the theory of Dirichlet forms, its applications to proving weak convergence of Markov processes and the recent application of this theory to the optimal scaling problem for the random walk Metropolis-Hastings algorithm for product targets (Zanella, Bédard, and Kendall 2017). In the second part of the thesis, we show that the framework of semimartingale limit theorems can also effectively be used to treat the optimal scaling problem for product targets. We prove the optimal scaling result on the random walk Metropolis-Hastings algorithm with product target under weaker conditions than in Zanella, Bédard, and Kendall 2017, and we give a proof of the optimal scaling result for the MALA algorithm with product target under weaker assumptions than in the original article (Gareth O. Roberts and J. S. Rosenthal 1998)

 

 

Vejleder:  Ernst Hansen
Censor:    Anders Rønn-Nielsen, CBS