Estimation of reaction rate constants using stochastic differential equations

7 Estimation of reaction rate constants using stochastic differential equations 

Although there are several techniques for estimating the reaction rate constants based upon the deterministic model, these methods are usually rather complicated, and the results cannot be statistically characterised. That is why from time to time estimates based upon one or another stochastic model are suggested. Such a suggestion has earlier been described under the name fluctuation-dissipation theorem , and similar methods have been presented by Mulloolly (1971, 1972, 1973), Hilden (1974), and Matis and Hartley (1971). 

Now we outline another method based upon a stochastic differential equation model of a certain internal noise of unspecified origin in a reaction not coming from the reaction itself. A possible way of doing this is to consider the stochastic differential equation 

The integral with respect to the Wiener process is taken using the Ito approach that has an important advantage over the Stratonovich approach, namely the integral in this case will be a martingale. Definitions and 

What is the reason for writing a model in the form (5.181) It turned out (Hangos Toth, 1988) that this description makes it easy to estimate the reaction rate constants, because the linear dependence of the right-hand side on the reaction rate constants can be utilised. The estimate can be explicitly given as 

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