RECURSIVE COMPUTATION OF THE INVARIANT DISTRIBUTION OF A DIFFUSION: THE CASE OF A WEAKLY MEAN REVERTING DRIFT

By Damien Lamberton, Gilles Pagès. 2003

87 citations recorded by the source corpus.

Subfields: Finance, Management Information Systems, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/cd492b20c1d1912471920abe7db4d50e677ef475

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. George Yin
2. Xiaoyue Li
3. Alain Oliviero Durmus
4. Arnak S. Dalalyan
5. Eric Moulines
6. Xuerong Mao
7. Chao Zhu
8. Ke Wang

In Management Information Systems

1. Arnak S. Dalalyan
2. Eric Moulines
3. Alain Oliviero Durmus

In Modeling and Simulation

1. George Yin
2. Xuerong Mao
3. Arnak S. Dalalyan
4. Eric Moulines
5. Xiaoyue Li
6. Alain Oliviero Durmus
7. Ke Wang
8. Meng Liu

Citations in the corpus

• Explicit numerical approximations for stochastic differential equations in finite and infinite horizons: truncation methods, convergence in pth moment, and stability (2019, background): “Lamberton & Pagès (2002, 2003) studied recursive stochastic algorithms with decreasing step sizes to approximate the invariant distribution for an Euler scheme under Lyapunov-type assumptions under the provision of the existence of such a Lyapunov function.”
• An adaptive scheme for the approximation of dissipative systems (2005, unknown): “The existence of the Lyapounov function V implies the regularity of the process ( x t ) t 0 so that the Echeverria-Weiss applies –although b has not sublinear growth–.”
• A Tail-Index Analysis of Stochastic Gradient Noise in Deep Neural Networks (2019, background): “Recent results on ULA [44,56] have shown that, the required number of iterations to achieve the invariant measure often grows exponentially with the dimension p .”
• Theoretical guarantees for approximate sampling from smooth and log‐concave densities (2014, background): “It can be traced back at least to Lamberton and Pagès (2002); see also Lemaire (2005) for an overview.”
• Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm (2015, background): “Compared to the related works by [23], [24], [25] and [26], we establish not only the weak convergence of the weighted empirical measure of the path to the target distribution but a much stronger convergence in total variation, similarly to [12], where the strongly log-concave case is considered.”
• High-dimensional Bayesian inference via the unadjusted Langevin algorithm (2016, background): “Lemma 24.”