Related papers: Bayesian Parameter Inference for Partially Observe…

Semi-discrete Runge-Kutta schemes for nonlinear diffusion equations of parabolic type are analyzed. Conditions are determined under which the schemes dissipate the discrete entropy locally. The dissipation property is a consequence of the…

Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…

In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…

We consider the problem of Bayesian inference for bi-variate data observed in time but with observation times which occur non-synchronously. In particular, this occurs in a wide variety of applications in finance, such as high-frequency…

We propose a straightforward and effective method for discretizing multi-dimensional diffusion processes as an extension of Milstein scheme. The new scheme is explicitly given and can be simulated using Gaussian variates, requiring the same…

Parameter inference for stochastic differential equations is challenging due to the presence of a latent diffusion process. Working with an Euler-Maruyama discretisation for the diffusion, we use variational inference to jointly learn the…

McKean-Vlasov stochastic differential equations (MVSDEs) describe systems whose dynamics depend on both individual states and the population distribution, and they arise widely in neuroscience, finance, and epidemiology. In many…

In this paper we take up Bayesian inference in general multivariate stable distributions. We exploit the representation of Matsui and Takemura (2009) for univariate projections, and the representation of the distributions in terms of their…

Microscopic processes on surfaces such as adsorption, desorption, diffusion and reaction of interacting particles can be simulated using kinetic Monte Carlo (kMC) algorithms. Even though kMC methods are accurate, they are computationally…

A class of evolution equations with nonlocal diffusion is considered in this work. These are integro-differential equations arising as models of propagation phenomena in continuum media with nonlocal interactions including neural tissue,…

In this paper, we are interested in deriving non-asymptotic error bounds for the multilevel Monte Carlo method. As a first step, we deal with the explicit Euler discretization of stochastic differential equations with a constant diffusion…

We analyse a Monte Carlo particle method for the simulation of the calibrated Heston-type local stochastic volatility (H-LSV) model. The common application of a kernel estimator for a conditional expectation in the calibration condition…

We consider the problem of parameter estimation for a class of continuous-time state space models. In particular, we explore the case of a partially observed diffusion, with data also arriving according to a diffusion process. Based upon a…

In this article we consider a Monte Carlo-based method to filter partially observed diffusions observed at regular and discrete times. Given access only to Euler discretizations of the diffusion process, we present a new procedure which can…

In this paper we consider Bayesian parameter inference associated to a class of partially observed stochastic differential equations (SDE) driven by jump processes. Such type of models can be routinely found in applications, of which we…

In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. This is a challenging problem which requires the use of advanced numerical schemes based upon…

This work gives the asymptotic error distribution of the stochastic Runge--Kutta (SRK) method of strong order $1$ applied to Stratonovich-type stochastic differential equations. For dealing with the implicitness introduced in the diffusion…

In this paper we consider the parameter estimation problem associated to partially-observed time changed SDEs, with observations that are given at discrete times. In particular we consider both likelihood and Bayesian estimation. We develop…

Discrete diffusion models have gained increasing attention for their ability to model complex distributions with tractable sampling and inference. However, the error analysis for discrete diffusion models remains less well-understood. In…

We present a highly efficient proximal Markov chain Monte Carlo methodology to perform Bayesian computation in imaging problems. Similarly to previous proximal Monte Carlo approaches, the proposed method is derived from an approximation of…