Related papers: Gibbs point processes on path space: existence, cl…
The aim of this paper is to shed light on the analysis of non-stationary time series by means of the method of diffusion entropy. For this purpose, we first study the case when infinitely many time series, as different realizations of the…
We consider a system of diffusion processes interacting through their empirical distribution. Assuming that the empirical average of a given observable can be observed at any time, we derive regularity and quantitative stability results for…
This paper introduces a framework for simulating finite dimensional representations of (jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in such a way that the sample path can be restored at any…
The symbiotic branching model describes a spatial population consisting of two types that are allowed to migrate in space and branch locally only if both types are present. We continue our investigation of the large scale behaviour of the…
In this paper we give an elementary proof of uniqueness of solutions to a gas-disk interaction system with diffusive boundary condition. Existence of near-equilibrium solutions for this type of systems with various boundary conditions has…
Noncolliding diffusion processes reported in the present paper are $N$-particle systems of diffusion processes in one-dimension, which are conditioned so that all particles start from the origin and never collide with each other in a finite…
We study a discrete-time interacting particle system with continuous state space which is motivated by a mathematical model for turnover through branching in actin filament networks. It gives rise to transient clusters reminiscent of actin…
The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, soil science, and biomedical engineering. The mathematical challenge in these type of…
We presented background information about various entropies in the literature. The pathway idea of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure and established connections to…
An infinite system of point particles placed in $\mathds{R}^d$ is studied. Its constituents perform random jumps with mutual repulsion described by a translation-invariant jump kernel and interaction potential, respectively. The pure states…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
Generative models on discrete state-spaces have a wide range of potential applications, particularly in the domain of natural sciences. In continuous state-spaces, controllable and flexible generation of samples with desired properties has…
We investigate the simple one-dimensional driven model, the totally asymmetric exclusion process, coupled to mutually interactive Langmuir kinetics. This model is motivated by recent studies on clustering of motor proteins on microtubules.…
In this work, we study convection-diffusion equations in the cases of bounded drifts and drifts induced by the gradient of a potential. We define a new notion of solution and prove its existence and uniqueness. Furthermore, we show the…
This work is devoted to the study of processes generated by random substitutions over a finite alphabet. We prove, under mild conditions on the substitution's rule, the existence of a unique process which remains invariant under the…
Denoising diffusion models have proven to be a flexible and effective paradigm for generative modelling. Their recent extension to infinite dimensional Euclidean spaces has allowed for the modelling of stochastic processes. However, many…
We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several…
Consider a spectrally positive Stable($1+\alpha$) process whose jumps we interpret as lifetimes of individuals. We mark the jumps by continuous excursions assigning "sizes" varying during the lifetime. As for Crump-Mode-Jagers processes…
We consider Gibbs distributions on permutations of a locally finite infinite set $X\subset\mathbb{R}$, where a permutation $\sigma$ of $X$ is assigned (formal) energy $\sum_{x\in X}V(\sigma(x)-x)$. This is motivated by Feynman's path…
We study a reaction-diffusion system on the real line, where the reactions of the species are given by one reversible reaction according to the mass-action law. We describe different positive limits at both sides of infinity and investigate…