3 problems

Let $X$ be the Lévy process considered above, with $\mathcal F$ its filtration, and let $R$ be an independence time belonging to $\overline{\sigma(X)}/\mathcal{B}_{[0,\infty]}$. Th…

Let $(\Omega,\mathcal G,P)$ be a probability space, and suppose there exists a random time $\tau$ whose dual predictable projection has the form … where $\Lambda$ is a nonnegative,…

Let $\tau$ be a random time, possibly a stopping time. Suppose that the conditional distribution process … is increasing, and let $**the martingale hazard process**$Lambda…