In this article we consider the approximation of expectations wrt probability distributions
associated to the solution of partial differential equations (PDEs); this scenario appears …

This thesis develops computationally efficient methodology in two areas. Firstly, we consider
a particularly challenging class of discretely observed continuous-time point-process …

We present a scalable approach to performing approximate fully Bayesian inference in
generic state space models. The proposed method is an alternative to particle MCMC that …

In this article we consider the filtering problem associated to partially observed diffusions,
with observations following a marked point process. In the model, the data form a point …

We consider a class of high‐dimensional spatial filtering problems, where the spatial
locations of observations are unknown and driven by the partially observed hidden signal …

This paper presents a new data assimilation (DA) scheme based on a sequential Markov
Chain Monte Carlo (SMCMC) DA technique [Ruzayqat et al. 2024] which is provably …

Process monitoring and control requires the detection of structural changes in a data stream
in real time. This article introduces an efficient sequential Monte Carlo algorithm designed …

We develop particle Gibbs samplers for static-parameter estimation in discretely observed
piecewise deterministic process (PDPs). PDPs are stochastic processes that jump randomly …

Are viral dynamics, the peer-to-peer propagation of ideas and trends, important in social
media systems, compared to external influence? Are such dynamics quantifiable? Are they …

On an incomplete financial market, the stocks are modeled as pure jump processes subject
to defaults. The exponential utility maximization problem is investigated characterizing the …