ESTIMATING DIFFUSION COEFFICIENTS FROM COUNT DATA: EINSTEIN-SMOLUCHOWSKI THEORY REVISITED

N. H. BINGHAM^{1} AND BRUCE DUNHAM^{2}

1Statistics Department, Birkbeck College (University of London), Malet Street, London WC1E 7HX, U.K.

2Mathematics Department, University of Nottingham, Nottingham NG7 2RD, U.K.

(Received November 21, 1995; revised June 27, 1996)

Abstract. The problem of estimating diffusion coefficients has been considered extensively in both discrete and continuous time. We consider here an approach based on counting occupation numbers of diffusing particles. The problem, and our approach, are motivated by statistical mechanics.

Key words and phrases: Diffusion, coverage process, regenerative phenomenon, Campbell’s theorem, infinite server queue, Einstein-Smoluchowski process, Avogadro’s number.