Diffusion process: Difference between revisions

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is a local martingale under <math>\mathbb{P}^{\xi,\tau}_{a;b}</math> for <math>t \ge \tau</math>, with <math>M_t^{[f]} = 0</math> for <math>t \le \tau</math>.
 
This family <math>\mathbb{P}^{\xi,\tau}_{a;b}</math> is called the <math>\mathcal{L}_{a;b}</math>-diffusion, where <math>\mathcal{L}_{a;b} = L_{a;b} + \frac{\partial}{\partial t}</math> is the time‐dependent infinitesimal generator.
 
== SDE Construction and Infinitesimal Generator ==