Stochastic reaction kinetics nonequilibrium thermodynamics of state-space

1 Stochastic reaction kinetics nonequilibrium thermodynamics of state-space 7 

Our starting point is the Kramers-Moyal-Stratonovich equation (5.13). Neglecting the higher-than-first-order conditional moments the drift equation is obtained  

Since g is a probability density function, and a deterministic initial condition has been assumed, the following conditions hold  

The unique solution of (5.67) satisfying the condition (5.68) is the 5, ) distribution, where x t) is the solution of the initial value problem 

The statement can be proved by solving (5.67) for the function g( ), and taking into consideration the condition (5.68). The theoretical basis of the procedure can be found in Hormander (1964), and the statement may be interpreted in four different ways. 

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