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An idea for evaluating transition probabilities in chemical reaction systemsis proposed, which is efficient for repeated calculations with various rateconstants. The idea is based on duality relations; instead of directtime-evolutions of the original reaction system, the dual process is dealtwith. Usually, if one changes rate constants of the original reaction system,the direct time-evolutions should be performed again, using the new rateconstants. On the other hands, only one solution of an extended dual processcan be re-used to calculate the transition probabilities for various rateconstant cases. The idea is demonstrated in a parameter estimation problem forthe Lotka-Volterra system.

Duality-based calculations for transition probabilities in stochastic chemical reactions