The subject of inverse problems in differential equations is of enormous practical importance, and has also generated substantial mathematical and computational innovation.Expand

The ergodic properties of SDEs, and various time discretizations for SDEs, are studied. The ergodicity of SDEs is established by using techniques from the theory of Markov chains on general state… Expand

Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes.… Expand

This book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numerical… Expand

These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian
approach to inverse problems in… Expand

We show that an implicit variant of Euler--Maruyama converges if the diffusion coefficient is globally Lipschitz, but the drift coefficient satisfies only a one-sided Lipschnitz condition; this is achieved by showing that the implicit method has bounded moments and may be viewed as an approximation to a perturbed SDE of the same form.Expand

We investigate the properties of the Hybrid Monte Carlo algorithm (HMC) in high dimensions.
HMC develops a Markov chain reversible w.r.t. a given target distribution . by using separable Hamiltonian… Expand

We show that the ensemble Kalman method for inverse problems provides a derivative-free optimization method with comparable accuracy to that achieved by traditional least-squares approaches.Expand