Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important
examples include gene expression and enzymatic processes in living cells. Such systems …

Approximate resolution of linear systems of differential equations with varying coefficients is
a recurrent problem, shared by a number of scientific and engineering areas, ranging from …

Diffusion models are recent state-of-the-art methods for image generation and likelihood
estimation. In this work, we generalize continuous-time diffusion models to arbitrary …

We present The Virtual Brain (TVB), a neuroinformatics platform for full brain network
simulations using biologically realistic connectivity. This simulation environment enables the …

During the seven years that elapsed between the first and second editions of the present
book, considerable progress was achieved in the area of financial modelling and pricing of …

For a function g (h), we write g (h)= O (hp) to mean that there exist constants h0> 0 and K> 0
(independent of h) such that| g (h)|< Khp for all| h|< h0. In words, this means that g (h) tends …

We present and analyse two implicit methods for Ito stochastic differential equations (SDEs)
with Poisson-driven jumps. The first method, SSBE, is a split-step extension of the backward …

The numerical approximation of stochastic partial differential equations (SPDEs),
specifically, stochastic evolution equations of the parabolic or hyperbolic type, encounters all …

Stochasticity is a key characteristic of intracellular processes such as gene regulation and
chemical signalling. Therefore, characterizing stochastic effects in biochemical systems is …

We identify effective stochastic differential equations (SDEs) for coarse observables of fine-
grained particle-or agent-based simulations; these SDEs then provide useful coarse …