相关论文: Simulation of conditioned diffusions

Diffusion processes are fundamental in modelling stochastic dynamics in natural sciences. Recently, simulating such processes on complicated geometries has found applications for example in biology, where toroidal data arises naturally when…

Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…

We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection sampling and, when applicable, returns the location of the path at a random…

The aim of this article is to provide a scheme for simulating diffusion processes evolving in one-dimensional discontinuous media. This scheme does not rely on smoothing the coefficients that appear in the infinitesimal generator of the…

We propose a computational method to simulate anomalous self-diffusion in a simple liquid. The method is based on a molecular dynamics simulation on which we impose the following two conditions: firstly, the inter-particle interaction is…

We present a conditional diffusion model - ConDiSim, for simulation-based inference of complex systems with intractable likelihoods. ConDiSim leverages denoising diffusion probabilistic models to approximate posterior distributions,…

Discrete element method simulations of confined bidisperse granular shear flows elucidate the balance between diffusion and segregation that can lead to either mixed or segregated states, depending on confining pressure. Results indicate…

In this paper, we prove a result of equivalence in law between a diffusion conditioned with respect to partial observations and an auxiliary process. By partial observations we mean coordinates (or linear transformation) of the process at a…

We propose a simpler derivation of the probability density function of Feller Diffusion using the Fourier Transform and solving the resulting equation via the Method of Characteristics. We also discuss simulation algorithms and confirm key…

We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the…

In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a…

We consider a general method for the approximation of the distribution of a process conditioned to not hit a given set. Existing methods are based on particle system that are failable, in the sense that, in many situations , they are not…

With a view to statistical inference for discretely observed diffusion models, we propose simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge simulation plays a fundamental role in likelihood and…

Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…

We present a direct numerical simulation method for investigating the dynamics of dispersed particles in a compressible solvent fluid. The validity of the simulation is examined by calculating the velocity relaxation of an impulsively…

We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…

In this paper we derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval, conditioned on the terminal state. The conditioning can be with respect to a fixed point…

Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…

As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…

Continuous diffusion models are commonly acknowledged to display a deterministic probability flow, whereas discrete diffusion models do not. In this paper, we aim to establish the fundamental theory for the probability flow of discrete…