After years' study in probability, I felt more and more happy with the construction of probability space, it's so simple seemingly but interesting that may be applied to many more areas rather than math.

Let’s review a little bit about the probability space in math. Given a space (\Omega, \mathbb{F}, \mathbb{P}), assume that there exists a r.v X s.t. \{\omega|X(\omega)>0\}\in\mathbb{F}, then we can measure the events \{X>0\} by using \mathbb{P}(X>0). What’s more, adding a time dimension to make it a stochastic process X_t(\omega), then we have properties like \mathbb{F}_t\subset\mathbb{F}_{t^+} and so on.

Secondly, let’s consider another fact, different people have different decisions when given tasks, why is that? That apparently depends on the knowledge we own, how do I relate this decision making base on probability space construction idea? This attracts me these days and I’ll post what I think later.

To be continued……


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