  This paper deals with the problem of estimating second-order parameter
sensitivities for stochastic reaction networks, where the reaction dynamics is
modeled as a continuous time Markov chain over a discrete state space.
Estimation of such second-order sensitivities (the Hessian) is necessary for
implementing the Newton-Raphson scheme for optimization over the parameter
space. To perform this estimation, Wolf and Anderson have proposed an efficient
finite-difference method, that uses a coupling of perturbed processes to reduce
the estimator variance. The aim of this paper is to illustrate that the same
coupling can be exploited to derive an exact representation for second-order
parameter sensitivity. Furthermore with this representation one can construct
an unbiased estimator which is easy to implement. The ideas contained in this
paper are extensions of the ideas presented in our recent papers on first-order
parameter sensitivity estimation.
