Related papers: A general moment expansion method for stochastic k…
This work is concerned with kinetic equations with velocity of constant magnitude. We propose a quadrature method of moments based on the Poisson kernel, called Poisson-EQMOM. The derived moment closure systems are well defined for all…
The Chemical Master Equation (CME) is used to stochastically model biochemical reaction networks, under the Markovian assumption. The low-order statistical moments induced by the CME are often the key quantities that one is interested in.…
The superiority of symplectic methods for stochastic Hamiltonian systems has been widely recognized, yet the probabilistic mechanism behind this superiority remains incompletely understood. This paper studies the superiority of symplectic…
Approximations based on moment-closure (MA) are commonly used to obtain estimates of the mean molecule numbers and of the variance of fluctuations in the number of molecules of chemical systems. The advantage of this approach is that it can…
The second moment method is a linear acceleration technique which couples the transport equation to a diffusion equation with transport-dependent additive closures. The resulting low-order diffusion equation can be discretized independent…
We demonstrate an approach to solving the coagulation equation that involves using a finite number of moments of the particle size distribution. This approach is particularly useful when only general properties of the distribution, and…
In this paper, we first extend the micro-macro decomposition method for multiscale kinetic equations from the BGK model to general collisional kinetic equations, including the Boltzmann and the Fokker-Planck Landau equations. The main idea…
Stein operators allow to characterise probability distributions via differential operators. Based on these characterisations, we develop a new method of point estimation for marginal parameters of strictly stationary and ergodic processes,…
This study concerns online inference (i.e., filtering) on the state of reaction networks, conditioned on noisy and partial measurements. The difficulty in deriving the equation that the conditional probability distribution of the state…
The phenomena of stochasticity in biochemical processes have been intriguing life scientists for the past few decades. We now know that living cells take advantage of stochasticity in some cases and counteract stochastic effects in others.…
The Langevin system subjected to non-Gaussian noise has been discussed, by using the second-order moment approach with two kinds of models for generating the noise. We have derived the effective differential equation (DE) for a variable…
The use of approximate solution techniques for the Chemical Master Equation is common practice for the analysis of stochastic chemical systems. Despite their widespread use, however, many such techniques rely on unverifiable assumptions and…
We introduce a simple stochastic system able to generate anomalous diffusion both for position and velocity. The model represents a viable description of the Fermi's acceleration mechanism and it is amenable to analytical treatment through…
We present a numerical discretisation of the coupled moment systems, previously introduced in Dahm and Helzel, which approximate the kinetic multi-scale model by Helzel and Tzavaras for sedimentation in suspensions of rod-like particles for…
Gradient descent-based optimization methods underpin the parameter training of neural networks, and hence comprise a significant component in the impressive test results found in a number of applications. Introducing stochasticity is key to…
We develop a recursive approach for deriving closed-form solutions to both conditional and unconditional moments of affine jump diffusions with state-independent jump intensities. Using these moment solutions, we construct closed-form…
In this paper, we propose a new approach for the time-discretization of the incompressible stochastic Stokes equations with multiplicative noise. Our new strategy is based on the classical Milstein method from stochastic differential…
A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the…
Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some…
The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates…