The Maximum Likelihood Estimation of Coefficient of Diffusion in a Birth and Diffusion Process

Abstract

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Remarks on Optimal Inference for Markov Branching Processes: A Sequential Approach

“…More specifically, if S(T) denotes the measurement on the characteristic for a single individual at time r, theprocess{S(t), r 2 O}hasstationaryindependentincrements,with S(t + 6) -S(t) distributed as normal with mean p8 andvariance d 6 . Adke & Dharmadhikari (1980) have discussed the problem of estimation of c2 when the underlying population grows according to a simple birth process, and hence is not subject to any threshold theorem. In this section we consider the general branching model of Section 6 as the population model and augment a Brownian motion component to each individual extant in the population.…”

Maximum likelihood estimation for a branching diffusion process

“…However, it is rare that observations in such detail are available. We therefore adopt the three sampling schemes suggested by Adke and Dharmadhikari [13]. We state below some of the properties of our process before defining the sampling schemes.…”

Asymptotic behavior of maximum likelihood estimators in a branching diffusion model

“…For an application of BDP in modelling cell movements we refer to Adke and Dharmadhikari (1980), and for an application to pollution air we refer to Gorostiza (1994).…”