An Efficient Finite Difference Method for Parameter Sensitivities of Continuous Time Markov Chains

An Efficient Finite Difference Method for Parameter Sensitivities of Continuous Time Markov Chains

We present an efficient finite difference method for the computation of parameter sensitivities that is applicable to a wide class of continuous time Markov chain models. The estimator for the method is constructed by coupling the perturbed and nominal processes in a natural manner, and the analysis proceeds by utilizing a martingale representation for the coupled processes. The variance of the...

Efficient Finite Difference Method for Computing Sensitivities of Biochemical Reactions

Sensitivity analysis of biochemical reactions aims at quantifying the dependence of the reaction dynamics on the reaction rates. The computation of the parameter sensitivities poses many computational challenges when taking stochastic noise into account. This paper proposes a new efficient finite difference method for computing parameter sensitivities of biochemical reactions. We employ propens...

An efficient finite difference time domain algorithm for band structure calculations of Phononic crystal

In this paper, a new algorithm for studying elastic wave propagation in the phononic crystals is presented. At first, the displacement-based forms of elastic wave equations are derived and then the forms are discretized using finite difference method. So the new algorithm is called the displacement-based finite difference time domain (DBFDTD). Three numerical examples are computed with this met...

Continuous Time Markov Chains

Discrete-time Markov chains are useful in simulation, since updating algorithms are easier to construct in discrete steps. They can also be useful as crude models of physical, biological, and social processes. However, in the physical and biological worlds time runs continuously, and so discrete-time mathematical models are not always appropriate. This is especially true in population biology –...

Continuous-time Markov Chains