scholarly journals Central Limit Theorems and Large Deviations for Additive Functionals of Reflecting Diffusion Processes

2015 ◽  
pp. 329-345 ◽  
Author(s):  
Peter W. Glynn ◽  
Rob J. Wang
Keyword(s):  
Large Deviations ◽  
Central Limit ◽  
Limit Theorems ◽  
Diffusion Processes ◽  
Central Limit Theorems ◽  
Additive Functionals

scholarly journals Central limit theorems for coupled particle filters

2020 ◽  
Vol 52 (3) ◽  
pp. 942-1001
Author(s):  
Ajay Jasra ◽  
Fangyuan Yu
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Particle Filters ◽  
Diffusion Processes ◽  
Asymptotic Variance ◽  
Sequential Estimation ◽  
Time Discretization ◽  
Central Limit Theorems ◽  
Forward Rate ◽  
Ml Estimation

AbstractIn this article we prove new central limit theorems (CLTs) for several coupled particle filters (CPFs). CPFs are used for the sequential estimation of the difference of expectations with respect to filters which are in some sense close. Examples include the estimation of the filtering distribution associated to different parameters (finite difference estimation) and filters associated to partially observed discretized diffusion processes (PODDP) and the implementation of the multilevel Monte Carlo (MLMC) identity. We develop new theory for CPFs, and based upon several results, we propose a new CPF which approximates the maximal coupling (MCPF) of a pair of predictor distributions. In the context of ML estimation associated to PODDP with time-discretization $\Delta_l=2^{-l}$ , $l\in\{0,1,\dots\}$ , we show that the MCPF and the approach of Jasra, Ballesio, et al. (2018) have, under certain assumptions, an asymptotic variance that is bounded above by an expression that is of (almost) the order of $\Delta_l$ ( $\mathcal{O}(\Delta_l)$ ), uniformly in time. The $\mathcal{O}(\Delta_l)$ bound preserves the so-called forward rate of the diffusion in some scenarios, which is not the case for the CPF in Jasra et al. (2017).

scholarly journals Rates of Convergence in Laplace’s Integrals and Sums and Conditional Central Limit Theorems

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 479
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Large Deviations ◽  
Central Limit ◽  
Limit Theorems ◽  
Rates Of Convergence ◽  
Central Limit Theorems ◽  
Error Terms

We obtained the exact estimates for the error terms in Laplace’s integrals and sums implying the corresponding estimates for the related laws of large number and central limit theorems including the large deviations approximation.

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