In this book, we study stochastic volatility models and methods of pricing, hedging, and
estimation. Among models, we will study models with heavy tails and long memory or long …

Estimation of parameters of a diffusion based on discrete time observations poses a difficult
problem due to the lack of a closed form expression for the likelihood. From a Bayesian …

Abstract Models of stochastic processes are widely used in almost all fields of science.
Theory validation, parameter estimation, and prediction all require model calibration and …

The identification of diffusion processes is challenging for many real-world systems with
sparsely sampled observation data. In this work, we propose a data augmentation-based …

Continuous-discrete smoothing of diffusions Page 1 Electronic Journal of Statistics Vol. 15 (2021)
4295–4342 ISSN: 1935-7524 https://doi.org/10.1214/21-EJS1894 Continuous-discrete …

We consider a nonlinear filtering problem whereby the signal obeys the stochastic Navier--
Stokes equations and is observed through a linear map** with additive noise. The setup is …

Suppose X is a multidimensional diffusion process. Assume that at time zero the state of X is
fully observed, but at time only linear combinations of its components are observed. That is …

Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task
that has prompted the development of a number of algorithms, mainly within the …

The Wright-Fisher diffusion is a fundamentally important model of evolution encompassing
genetic drift, mutation, and natural selection. Suppose you want to infer the parameters …

ABSTRACT A continuous-time Markov process X can be conditioned to be in a given state at
a fixed time T> 0 using Doob's h-transform. This transform requires the typically intractable …