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Interacting particle systems are known for their ability to generate large-scale self-organized structures from simple local interaction rules between each agent and its neighbors. In addition to studying their emergent behavior, a main…
Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order $\alpha$ ($0 < \alpha < 1$). The solution regularity in the Sobolev space is revisited, and new regularity results in the…
We study recursive maximum likelihood estimation for stochastic interacting particle systems based on continuous observation of a single particle. In this regime, consistent estimation of the finite-particle log-likelihood is not possible,…
We study a nonlinear branching diffusion process in the sense of McKean, i.e., where particles are subjected to a mean-field interaction. We consider first a strong formulation of the problem and we provide an existence and uniqueness…
We consider the problem of Bayesian estimation of static parameters associated to a partially and discretely observed diffusion process. We assume that the exact transition dynamics of the diffusion process are unavailable, even up-to an…
We study a system of $N$ interacting particles on $\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs…
This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…
This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formulation of particle systems originally due to Tanaka that…
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…
We consider a sequence of systems of Hawkes processes having mean field interactions in a diffusive regime. The stochastic intensity of each process is a solution of a stochastic differential equation driven by N independent Poisson random…
Sources of variability in experimentally derived data include measurement error in addition to the physical phenomena of interest. This measurement error is a combination of systematic components, originating from the measuring instrument,…
This paper investigates the estimation of the interaction function for a class of McKean-Vlasov stochastic differential equations. The estimation is based on observations of the associated particle system at time $T$, considering the…
Variational inequalities are a universal optimization paradigm that incorporate classical minimization and saddle point problems. Nowadays more and more tasks require to consider stochastic formulations of optimization problems. In this…
In this article we consider the filtering problem associated to partially observed diffusions, with observations following a marked point process. In the model, the data form a point process with observation times that have its intensity…
The random batch Ewald (RBE) is an efficient and accurate method for molecular dynamics (MD) simulations of physical systems at the nano-/micro- scale. The method shows great potential to solve the computational bottleneck of long-range…
Interacting particle systems are in frequent use to model collective behaviour in various situations and applications. For many systems, the interaction between the agents is restricted to an underlying network structure and often, the…
This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…