This paper introduces a framework for simulating finite dimensional representations of
(jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in …

This paper develops the first class of algorithms that enable unbiased estimation of steady-
state expectations for multidimensional reflected Brownian motion. In order to explain our …

Consider a multidimensional diffusion process X={X(t):t∈0,1\}. Let ε>0 be a deterministic,
user defined, tolerance error parameter. Under standard regularity conditions on the drift …

Diffusions are a fundamental class of models in many fields, including finance, engineering,
and biology. Simulating diffusions is challenging as their sample paths are infinite …

We present the first exact simulation method for multidimensional reflected Brownian motion
(RBM). Exact simulation in this setting is challenging because of the presence of correlated …

In this thesis we develop computationally efficient methods to simulate finite dimensional
representations of (jump) diffusion and (jump) diffusion bridge sample paths over finite …

Using marked Dirichlet processes we characterise the law of the convex minorant of the
meander for a certain class of Lévy processes, which includes subordinated stable and …

Consider a fractional Brownian motion (fBM) BH={BH (t): t∈[0, 1]} with Hurst index H∈(0, 1).
We construct a probability space supporting both BH and a fully simulatable process B^∈ H …

For rare events described in terms of Markov processes, truly unbiased estimation of the rare
event probability generally requires the avoidance of numerical approximations of the …

In this paper we uniformly approximate the trajectories of the Cox–Ingersoll–Ross (CIR)
process. At a sequence of random times the approximate trajectories will be even exact. In …