Consider a probability space $(\Omega,\mathcal{F},\mathbb{P})$ with two filtrations $(\mathcal{F}_t)_{t\geq0}$ and $(\mathcal{G}_t)_{t\geq0}$. The book Credit Risk: Modeling, Valuation, and Hedging by Tomasz R. Bielecki and Marek Rutkowski uses the notation $\mathcal{F}_t\vee\mathcal{G}_t$ for the joint filtration of $\mathcal{F}_t$ and $\mathcal{G}_t$ without giving a definition. So I wonder what is the joint filtration? Is it defined as follows, i.e. the $\sigma$-field generated by the union of $\mathcal{F}_t$ and $\mathcal{G}_t$? $$ \mathcal{F}_t\vee\mathcal{G}_t=\sigma(\mathcal{F_t}\cup\mathcal{G}_t) $$
2026-03-27 02:39:53.1774579193
What is joint filtration?
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