Related papers: Moate Simulation of Stochastic Processes
Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…
Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number…
The slow processes of metastable stochastic dynamical systems are difficult to access by direct numerical simulation due the sampling problem. Here, we suggest an approach for modeling the slow parts of Markov processes by approximating the…
For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of different minimizers. To adapt this for optimization over a space…
Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…
A novel method is presented to compute the exit time for the stochastic simulation algorithm. The method is based on the addition of a series of random variables and is derived using the convolution theorem. The final distribution is…
The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…
In this paper, we propose and analyze a new stochastic homogenization method for diffusion equations with random and fast oscillatory coefficients. In the proposed method, the homogenized solutions are sought through a two-stage procedure.…
Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area because such models allow a parsimonious representation of multivariate stochastic volatility. Bayesian…
In this paper, an alternative Discrete skew Logistic distribution is proposed, which is derived by using the general approach of discretizing a continuous distribution while retaining its survival function. The properties of the…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an It\^o stochastic differential equation conditional on an observation taken at a fixed future time-point. Such…
Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
This paper presents a robust version of the stratified sampling method when multiple uncertain input models are considered for stochastic simulation. Various variance reduction techniques have demonstrated their superior performance in…
The Diffusion Monte Carlo method with constant number of walkers, also called Stochastic Reconfiguration as well as Sequential Monte Carlo, is a widely used Monte Carlo methodology for computing the ground-state energy and wave function of…
We recently demonstrated that standard fixed-time lattice random-walk models cannot be modified to properly represent biased diffusion processes in more than two dimensions. The origin of this fundamental limitation appears to be the fact…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the…
Recently, hybrid models have emerged that combine microscopic and mesoscopic regimes in a single stochastic reaction-diffusion simulation. Microscopic simulations track every individual molecule and are generally more accurate. Mesoscopic…