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We consider adaptive Bayesian estimation of both drift and diffusion coefficient parameters for ergodic multidimensional diffusion processes based on sampled data. Under a general condition on the discretization step of the sampled data, three kinds of adaptive Bayes type estimators are proposed...

This paper is concerned with parameter estimation in linear and non-linear Itô type stochastic differential equations using Markov chain Monte Carlo (MCMC) methods. The MCMC methods studied in this paper are the Metropolis–Hastings and Hamiltonian Monte Carlo (HMC) algorithms. In these kind...

This article investigates the application of depth estimators to crack growth models in construction engineering. Many crack growth models are based on the Paris–Erdogan equation which describes crack growth by a deterministic differential equation. By introducing a stochastic error term,...