Related papers: Parameter Estimation for the McKean-Vlasov Stochas…
Delattre et al. (2013) considered n independent stochastic differential equations (SDEs), where in each case the drift term is associated with a random effect, the distribution of which depends upon unknown parameters. Assuming the…
We introduce and analyse a continuum model for an interacting particle system of Vicsek type. The model is given by a non-linear kinetic partial differential equation (PDE) describing the time-evolution of the density $f_t$, in the single…
The stochastic motions of a diffusing particle contain information concerning the particle's interactions with binding partners and with its local environment. However, accurate determination of the underlying diffusive properties, beyond…
This paper is a survey of recent contributions on estimation in stochastic differential equations with mixed-effects. These models involve N stochastic differential equations with common drift and diffusion functions but random parameters…
We propose a novel gradient-based online optimization framework for solving stochastic programming problems that frequently arise in the context of cyber-physical and robotic systems. Our problem formulation accommodates constraints that…
In this article we investigate consistency and asymptotic normality of the maximum likelihood and the posterior distribution of the parameters in the context of state space stochastic differential equations (SDEs). We then extend our…
We present results on parameter estimation and non-parameter estimation of the linear partially observed Gaussian system of stochastic differential equations. We propose new one-step estimators which have the same asymptotic properties as…
We present a comprehensive discretization scheme for linear and nonlinear stochastic differential equations (SDEs) driven by either Brownian motions or $\alpha$-stable processes. Our approach utilizes compound Poisson particle…
We propose a novel approach to numerically approximate McKean-Vlasov stochastic differential equations (MV-SDE) using stochastic gradient descent (SGD) while avoiding the use of interacting particle systems (IPS) {and the associated…
In this paper, we consider the problem of jointly performing online parameter estimation and optimal sensor placement for a partially observed infinite dimensional linear diffusion process. We present a novel solution to this problem in the…
We study approximate maximum likelihood estimators (MLEs) for the parameters of the widely used Heston stock and volatility stochastic differential equations (SDEs). We compute explicit closed form estimators maximizing the discretized…
In this article, we study an interacting particle system in the context of epidemiology where the individuals (particles) are characterized by their position and infection state. We begin with a description at the microscopic level where…
We study the convergence of the empirical measure of moderately interacting particle systems subject to singular forces derived by Lennard-Jones potential. Although the classical Lennard-Jones force is widely used in molecular dynamics,…
We consider covariance parameter estimation for a Gaussian process under inequality constraints (boundedness, monotonicity or convexity) in fixed-domain asymptotics. We address the estimation of the variance parameter and the estimation of…
We study the problem of parameter estimation using maximum likelihood for fast/slow systems of stochastic differential equations. Our aim is to shed light on the problem of model/data mismatch at small scales. We consider two classes of…
Stochastic interacting particle systems are widely used to model collective phenomena across diverse fields, including statistical physics, biology, and social dynamics. The McKean-Vlasov equation arises as the mean-field limit of such…
In this paper, we study well-posedness of random periodic solutions of stochastic differential equations (SDEs) of McKean-Vlasov type driven by a two-sided Brownian motion, where the random periodic behaviour is characterised by the…
We consider in this work the convergence of a split-step Euler type scheme (SSM) for the numerical simulation of interacting particle Stochastic Differential Equation (SDE) systems and McKean-Vlasov Stochastic Differential Equations…
This paper establishes an indirect approximation theorem for the most probable transition pathway of a stochastic interacting particle system in the mean-field framework. This paper studied the problem of indirect approximation of the most…
In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of…