Two-particle models for the estimation of the mean and standard deviation of concentrations in coastal waters

Abstract

In this paper we study the mean and standard deviation of concentrations using random walk models. Two-particle models that take into account the space correlation of the turbulence are introduced and some properties of the distribution of the particle concentration are studied. In order to reduce the CPU time of the calculation a new estimator based on reverse time diffusion is applied. This estimator has been recently introduced by Milstein et al. (Bernoulli 10(2):281-312, 2004). Some numerical aspects of the implementation are discussed for relatively simple test problems. Finally, a realistic application to predict the spreading of the pollutant in the Dutch coastal zone is described.

Forward and reverse representations for Markov chains

“…It is shown that this forward-reverse density estimator (FRE) is basically root-N consistent in any dimension, this in contrast to the Parzen-Rosenblatt estimator which has accuracy N −1/(4+d) for dimension d. The forward-reverse estimator has turned out to be very useful for many practical applications. For example, in van den Berg, Heemink, Lin, Schoenmakers [1], Spivakovskaya, Heemink, Milstein, Schoenmakers [20], and Spivakovskaya, Heemink, Schoenmakers [21], the FRE is applied successfully to the estimation of pollutant concentrations in small coastal water regions, which are caused by a certain calamity at another place. In the latter applications the pollutants are modelled by a diffusion process.…”

Simulation of forward-reverse stochastic representations for conditional diffusions

“…However, by studying the process conditioned on starting in A and ending in B, one can efficiently observe on which paths the configuration typically travels from A to B. Other possible applications appear in the field of stochastic environmental models, for instance, regarding the concentration evolutions of pollution in water; for example see Spivakovskaya, Heemink and Schoenmakers (2007) and references therein for a related problem. Several approaches for simulation of diffusion bridges have already been studied in the literature.…”