Related papers: Theoretical analysis and simulation methods for Ha…
We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics.…
We propose a fast and efficient estimation method that is able to accurately recover the parameters of a d-dimensional Hawkes point-process from a set of observations. We exploit a mean-field approximation that is valid when the…
Discrete diffusion models (DDMs) are a powerful class of generative models for categorical data, but they typically require many function evaluations for a single sample, making inference expensive. Existing acceleration methods either rely…
As a counterpoint to classical stochastic particle methods for linear diffusion equations, we develop a deterministic particle method for the weighted porous medium equation (WPME) and prove its convergence on bounded time intervals. This…
New sampling algorithms based on simulating continuous-time stochastic processes called piece-wise deterministic Markov processes (PDMPs) have shown considerable promise. However, these methods can struggle to sample from multi-modal or…
We characterise the convergence of a certain class of discrete time Markov processes toward locally Feller processes in terms of convergence of associated operators. The theory of locally Feller processes is applied to L\'evy-type processes…
Hawkes processes are a popular framework to model the occurrence of sequential events, i.e., occurrence dynamics, in several fields such as social diffusion. In real-world scenarios, the inter-arrival time among events is irregular.…
In this paper, we aim to study the diffusion approximation for multi-scale McKean-Vlasov stochastic differential equations. More precisely, we prove the weak convergence of slow process $X^\varepsilon$ in $C([0,T];\mathbb{R}^n)$ towards the…
Penalized estimation methods for diffusion processes and dependent data have recently gained significant attention due to their effectiveness in handling high-dimensional stochastic systems. In this work, we introduce an adaptive…
We prove a Large Deviation Principle for Piecewise Deterministic Markov Processes (PDMPs). This is an asymptotic estimate for the probability of a trajectory in the large size limit. Explicit Euler-Lagrange equations are determined for…
Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple…
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…
In this note we prove the strong Feller property of a strong Markov quasi diffusion process corresponding to an elliptic operator with merely bounded measurable coefficients. We also prove H\"older continuity of harmonic functions…
In this paper, we provide strong $L_2$-rates of approximation of the integral-type functionals of Markov processes by integral sums. We improve the method developed in [2]. Under assumptions on the process formulated only in terms of its…
Many chemical reactions and molecular processes occur on timescales that are significantly longer than those accessible by direct simulation. One successful approach to estimating dynamical statistics for such processes is to use many short…
We introduce a nonlinear modification of the classical Hawkes process, which allows inhibitory couplings between units without restrictions. The resulting system of interacting point processes provides a useful mathematical model for…
We prove the convergence of the law of grid-valued random walks, which can be seen as time-space Markov chains, to the law of a general diffusion process. This includes processes with sticky features, reflecting or absorbing boundaries and…
The Hawkes model is a past-dependent point process, widely used in various fields for modeling temporal clustering of events. Extending this framework, the multidimensional marked Hawkes process incorporates multiple interacting event types…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods…