Scaling and Convergence to the Diffusion Process

Consider the microscopic stochastic equation for the particle position X (t ). 

3 Random Walks and Mesoscopic Reaction-Transport Equations Non-Markov CTRW 

Before dealing with the general stochastic equation (3.228), it is useful for fixing the basic ideas to discuss a relatively simple example. Consider the equation for the particle position X(t)  

Let us apply the scaling idea and determine the behavior of the rescaled particle 

For the general stochastic equation (3.228), the rescaled particle position X (f) = 

---