Numerical Methods for Solving Stochastic Models

In Section 4.2 we have shown that stochastic models present a good adaptability to numerical solving. In the opening line we asserted that it is not difficult to observe the simplicity of the numerical transposition of the models based on poly stochastic chains (see Section 4.1.1). As far as recursion equations describe the model, the numerical transposition of these equations can be written directly, without any special preparatives. 

When a stochastic model is described by a continuous polystochastic process, the numerical transposition can be derived by the classical procedure that change the derivates to their discrete numerical expressions related with a space discretisation of the variables. An indirect method can be used with the recursion equations, which give the links between the elementary states of the process. 

The following examples detail the numerical transposition of some stochastic models. The numerical state of a stochastic model allows the process simulation. 

Indeed, we can easily produce the evolution of the outputs of the process when the univocity conditions and parameters of the process are correctly chosen. 

The second example discusses the numerical transposition of the asymptotic models based on poly stochastic chains (see Section 4.4.1.1) where to compute the limit transition probabilities, we must solve the system ePek = 

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