DeepAI AI Chat
Log In Sign Up

Convergence of diffusions and their discretizations: from continuous to discrete processes and back

by   De Bortoli Valentin, et al.

In this paper, we establish new quantitative convergence bounds for a class of functional autoregressive models in weighted total variation metrics. To derive this result, we show that under mild assumptions explicit minorization and Foster-Lyapunov drift conditions hold. Our bounds are then obtained adapting classical results from Markov chain theory. To illustrate our results we study the geometric ergodicity of Euler-Maruyama discretizations of diffusion with covariance matrix identity. Second, we provide a new approach to establish quantitative convergence of these diffusion processes by applying our conclusions in the discrete-time setting to a well-suited sequence of discretizations whose associated stepsizes decrease towards zero.


Discrete sticky couplings of functional autoregressive processes

In this paper, we provide bounds in Wasserstein and total variation dist...

Uniform minorization condition and convergence bounds for discretizations of kinetic Langevin dynamics

We study the convergence in total variation and V-norm of discretization...

Unajusted Langevin algorithm with multiplicative noise: Total variation and Wasserstein bounds

In this paper, we focus on non-asymptotic bounds related to the Euler sc...

On the geometric convergence for MALA under verifiable conditions

While the Metropolis Adjusted Langevin Algorithm (MALA) is a popular and...

Quantitative convergence rates for reversible Markov chains via strong random times

Let (X_t) be a discrete time Markov chain on a general state space. It i...

High-dimensional MCMC with a standard splitting scheme for the underdamped Langevin diffusion

The efficiency of a markov sampler based on the underdamped Langevin dif...

On the rate of convergence for the autocorrelation operator in functional autoregression

We consider the problem of estimating the autocorrelation operator of an...