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Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by…
We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…
Quantum computers are expected to have substantial impact on the finance industry, as they will be able to solve certain problems considerably faster than the best known classical algorithms. In this article we describe such potential…
A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations…
GPU computing has become popular in computational finance and many financial institutions are moving their CPU based applications to the GPU platform. Since most Monte Carlo algorithms are embarrassingly parallel, they benefit greatly from…
We consider a class of discrete time stochastic control problems motivated by some financial applications. We use a pathwise stochastic control approach to provide a dual formulation of the problem. This enables us to develop a numerical…
Computer simulation plays a central role in modern day materials science. The utility of a given computational approach depends largely on the balance it provides between accuracy and computational cost. Molecular crystals are a class of…
We report the application of the Monte Carlo simulation to phase separation dynamics. First, we deal with the phase separation under shear flow. The thermal effect on the phase separation is discussed, and the anisotropic growth exponents…
Statistical inference for discretely observed jump-diffusion processes is a complex problem which motivates new methodological challenges. Thus existing approaches invariably resort to time-discretisations which inevitably lead to…
Fractional processes have gained popularity in financial modeling due to the dependence structure of their increments and the roughness of their sample paths. The non-Markovianity of these processes gives, however, rise to conceptual and…
We introduce a flexible method to simultaneously infer both the drift and volatility functions of a discretely observed scalar diffusion. We introduce spline bases to represent these functions and develop a Markov chain Monte Carlo…
Background: Monte Carlo simulations of diffusion are commonly used as a model validation tool as they are especially suitable for generating the diffusion MRI signal in complicated tissue microgeometries. New method: Here we describe the…
The task of accurately locating fluid phase boundaries by means of computer simulation is hampered by problems associated with sampling both coexisting phases in a single simulation run. We explain the physical background to these problems…
This paper develops and analyzes an efficient numerical method for solving elliptic partial differential equations, where the diffusion coefficients are random perturbations of deterministic diffusion coefficients. The method is based upon…
We construct Monte Carlo methods for the $L^2$-approximation in Hilbert spaces of multivariate functions sampling no more than $n$ function values of the target function. Their errors catch up with the rate of convergence and the…
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 computational statistics community. We propose a new direction,…
An efficient Path Integral Monte Carlo procedure is proposed to simulate the behavior of quantum many-body dissipative systems described within the framework of the influence functional. Thermodynamic observables are obtained by Monte Carlo…
We propose in this work a Monte Carlo method for three dimensional scalar radiative transfer equations with non-integrable, space-dependent scattering kernels. Such kernels typically account for long-range statistical features, and arise…
The Multilevel Monte Carlo (MLMC) approach usually works well when estimating the expected value of a quantity which is a Lipschitz function of intermediate quantities, but if it is a discontinuous function it can lead to a much slower…
This paper proposes a new theory and methodology to tackle the problem of unifying distributed analyses and inferences on shared parameters from multiple sources, into a single coherent inference. This surprisingly challenging problem…