# A stochastic evolution equation arising from the fluctuations of a class of interacting particle systems

@article{Kurtz2004ASE, title={A stochastic evolution equation arising from the fluctuations of a class of interacting particle systems}, author={Thomas G. Kurtz and Jie Xiong}, journal={Communications in Mathematical Sciences}, year={2004}, volume={2}, pages={325-358} }

In an earlier paper, we studied the approximation of solutions V (t) to a class of SPDEs by the empirical measure V n (t) of a system of n interacting difiusions. In the present paper, we consider a central limit type problem, showing that p n(V n iV ) converges weakly, in the dual of a nuclear space, to the unique solution of a stochastic evolution equation. Analogous results in which the difiusions that determine V n are replaced by their Euler approximations are also discussed.

## 50 Citations

### Central limit results for jump diffusions with mean field interaction and a common factor

- Mathematics
- 2014

ABSTRACT A system of N weakly interacting particles whose dynamics is given in terms of jump-diffusions with a common factor is considered. The common factor is described through another…

### Gaussian fluctuations for interacting particle systems with singular kernels

- Mathematics
- 2021

Abstract. We consider the asymptotic behaviour of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove that the sequence of fluctuation…

### Fluctuation Limit for Interacting Diffusions with Partial Annihilations Through Membranes

- Mathematics
- 2014

We study fluctuations of the empirical processes of a non-equilibrium interacting particle system consisting of two species over a domain that is recently introduced in Chen and Fan (Ann Probab, to…

### Fluctuation Limit for Interacting Diffusions with Partial Annihilations Through Membranes

- MathematicsJournal of Statistical Physics
- 2016

We study fluctuations of the empirical processes of a non-equilibrium interacting particle system consisting of two species over a domain that is recently introduced in Chen and Fan (Ann Probab, to…

### Numerical solution for a class of SPDEs over bounded domains

- Mathematics
- 2014

Parabolic stochastic partial differential Equations (SPDEs) with multiplicative noise play a central rôle in nonlinear filtering. More precisely, the conditional distribution of a partially observed…

### Numerical solutions for a class of SPDEs over bounded domains

- Mathematics
- 2007

The optimal filter for a bounded signal with reflecting boundary is approximated by the (un-weighted) empirical measure of a finite interacting particle system. The main motivation of this…

### Long-time behaviour of stochastic Hamilton-Jacobi equations

- Mathematics
- 2022

The long-time behavior of stochastic Hamilton-Jacobi equations is analyzed, including the stochastic mean curvature ﬂow as a special case. In a variety of settings, new and sharpened results are…

### Fluctuation analysis for particle-based stochastic reaction-diffusion models

- Mathematics
- 2022

. Recent works have derived and proven the large-population mean-ﬁeld limit for several classes of particle-based stochastic reaction-diﬀusion (PBSRD) models. These limits correspond to systems of…

### Central limit theorem for a spatial stochastic epidemic model with mean field interaction

- Mathematics
- 2022

. 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…

## References

SHOWING 1-10 OF 45 REFERENCES

### Asymptotic behavior of a system of interacting nuclear-space-valued stochastic differential equations driven by Poisson random measures

- Mathematics
- 1994

In this paper we study a system of interacting stochastic differential equations taking values in duals of nuclear spaces driven by Poisson random measures. We also consider the McKean-Vlasov…

### On a Class of Discrete Generation Interacting Particle Systems

- Mathematics
- 2001

The asymptotic behavior of a general class of discrete generation interacting particle systems is discussed. We provide L p -mean error estimates for their empirical measure on path space and present…

### Convergence of a Branching Particle Method to the Solution of the Zakai Equation

- MathematicsSIAM J. Appl. Math.
- 1998

A sequence of branching particle systems Un convergent in distribution to the solution of the Zakai equation is constructed, which can be used to solve numerically the filtering problem.

### Rate of convergence of a stochastic particle method for the Kolmogorov equation with variable coefficients

- Mathematics
- 1994

In a recent paper, E.G. Puckett proposed a stochastic particle method for the non linear diffusion-reaction P.D.E in [0,T] x R (the so-called "KPP" (Kolmogorov-Petrovskii-Piskunov) equation) :where…

### Interacting particle systems approximations of the Kushner-Stratonovitch equation

- MathematicsAdvances in Applied Probability
- 1999

In this paper we consider the continuous-time filtering problem and we estimate the order of convergence of an interacting particle system scheme presented by the authors in previous works. We will…

### Numerical Solutions for a Class of SPDEs with Application to Filtering

- Mathematics, Computer Science
- 2001

A simulation scheme for a class of nonlinear stochastic partial differential equations is proposed and error bounds for the scheme are derived and the results can be applied to nonlinear filtering problems.

### A particle approximation of the solution of the Kushner–Stratonovitch equation

- Mathematics
- 1998

Abstract. We construct a sequence of branching particle systems αn convergent in measure to the solution of the Kushner–Stratonovitch equation. The algorithm based on this result can be used to solve…

### Propagation of chaos and the McKean-Vlasov equation in duals of nuclear spaces

- Mathematics
- 1990

An interacting system ofn stochastic differential equations taking values in the dual of a countable Hilbertian nuclear space is considered. The limit (in probability) of the sequence of empirical…

### Propagation of chaos and fluction for a system of weakly interacting white noise driven parabolic spde's

- Mathematics
- 1996

We investigate the asymptotic behaviour of a system of N weakly interacting parabolic SPDE's when N become large.In particular we study a law of number (propagation of chaos) and the central limit…