Related papers: First-passage time for PDifMPs: an Exact simulatio…

Many problems in physics, biology, and economics depend upon the duration of time required for a diffusing particle to cross a boundary. As such, calculations of the distribution of first passage time, and in particular the mean first…

The study of time-inhomogeneous Markov jump processes is a traditional topic within probability theory that has recently attracted substantial attention in various applications. However, their flexibility also incurs a substantial…

We present a new efficient method for Monte Carlo simulations of diffusion-reaction processes. First introduced by us in [Phys. Rev. Lett., 97:230602, 2006], the new algorithm skips the traditional small diffusion hops and propagates the…

The aim of this paper is to investigate how the correlation properties of a stationary Markovian stochastic processes affect the First Passage Time distribution. First Passage Time issues are a classical topic in stochastic processes…

An adpative integration technique for time advancement of particle motion in the context of coupled computational fluid dynamics (CFD) - discrete element method (DEM) simulations is presented in this work. CFD-DEM models provide an accurate…

In this paper, we study the asymptotic of exit problem for controlled Markov diffusion processes with random jumps and vanishing diffusion terms, where the random jumps are introduced in order to modify the evolution of the controlled…

We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class…

As a highly expressive generative model, diffusion models have demonstrated exceptional success across various domains, including image generation, natural language processing, and combinatorial optimization. However, as data distributions…

We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete…

In Multiple Object Tracking, objects often exhibit non-linear motion of acceleration and deceleration, with irregular direction changes. Tacking-by-detection (TBD) trackers with Kalman Filter motion prediction work well in…

The time of the first occurrence of a threshold crossing event in a stochastic process, known as the first passage time, is of interest in many areas of sciences and engineering. Conventionally, there is an implicit assumption that the…

Drift diffusion models (DDMs) have found widespread use in computational neuroscience and other fields. They model evidence accumulation in simple decision tasks as a stochastic process drifting towards a decision barrier. In models where…

We study the similarities and differences between different models concerning subdiffusion. More particularly, we calculate first passage time (FPT) distributions for subdiffusion, derived from Greens' functions of nonlinear equations…

Direct simulation of the von Neumann dynamics for a general (pure or mixed) quantum state can often be expensive. One prominent example is the real-time time-dependent density functional theory (rt-TDDFT), a widely used framework for the…

Diffusion and flow matching models have significantly advanced media generation, yet their design space is well-explored, somewhat limiting further improvements. Concurrently, autoregressive (AR) models, particularly those generating…

Accurate knowledge of the properties of hydrogen at high compression is crucial for astrophysics (e.g. planetary and stellar interiors, brown dwarfs, atmosphere of compact stars) and laboratory experiments, including inertial confinement…

Noise-induced phase transitions are common in various complex systems, from physics to biology. In this article, we investigate the emergence of crucial events in noise-induced phase transition processes and their potential significance for…

We study diffusion with a bias towards a target node in networks. This problem is relevant to efficient routing strategies in emerging communication networks like optical networks. Bias is represented by a probability $p$ of the…

Diffusion Probabilistic Models (DPMs) have demonstrated exceptional capability of generating high-quality and diverse images, but their practical application is hindered by the intensive computational cost during inference. The DPM…

This study introduces a novel point-wise diffusion model that processes spatio-temporal points independently to efficiently predict complex physical systems with shape variations. This methodological contribution lies in applying forward…