The Solution of Stochastic Models with Analytical Methods

The Solution of Stochastic Models with Analytical Methods 

Examples 4.2 and 4.3 and the models from Section 4.4 show that the stochastic models can frequently be described mathematically by an assembly of differential partial equations. 

The core of a continuous stochastic model can be written as Eq. (4.150). Here, P(z,t) and a(z), b(z), c(z) are quadratic matrices and L is one linear operator with action on the matrix P(z,t). In the mentioned equation, f(z) is a vector with a length equal to the matrix P(z,t). In this model, z can be extended to a two- or a three-dimensional displacement  

This mathematical model has to be completed with realistic univocity conditions. In the literature, a large group of stochastic models derived from the model described above (4.150), have already been solved analytically. So, when we have a new model, we must first compare it to a known model with an analytical solution 

The analysis of the univocity conditions attached to the model shows that, here, we have an unsteady model where nonsymmetrical conditions are dominant. 

---