Publications [#316661] of James H. Nolen

Papers Published

1. Nolen, J, Normal approximation for the net flux through a random conductor, Stochastic Partial Differential Equations: Analysis and Computations, vol. 4 no. 3 (2015), pp. 439-476, Springer Nature, ISSN 2194-0401 [2186], [doi]
   (last updated on 2024/04/25)

   Abstract:
   We consider solutions of an elliptic partial differential equation in Rd with a stationary, random conductivity coefficient. The boundary condition on a square domain of width L is chosen so that the solution has a macroscopic unit gradient. We then consider the average flux through the domain. It is known that in the limit L →∞, this quantity converges to a deterministic constant, almost surely. Our main result is about normal approximation for this flux when L is large: we give an estimate of the Kantorovich–Wasserstein distance between the law of this random variable and that of a normal random variable. This extends a previous result of the author (Probab Theory Relat Fields, 2013. doi:10.1007/s00440-013-0517-9) to a much larger class of random conductivity coefficients. The analysis relies on elliptic regularity, on bounds for the Green’s function, and on a normal approximation method developed by Chatterjee (Ann Probab 36:1584–1610, 2008) based on Stein’s method.