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I seek literature that makes a rigorous treatment of counting processes. In particular im interested in a precise treatment of the conditional intensity $\lambda_t$ which is often informally defined ...

Let's consider a function $\Psi\in \mathcal{C}_B(\mathcal{C}[t,T])$ continuous and bounded \begin{align*} \Psi \colon \mathcal{C}[t,T] \longrightarrow [0,+\infty) \end{align*} Then my question is:...

Let $(Y_t)_{t\ge0}$ be a time-homogeneous Markov process with transition semigroup $(\kappa_t)_{t\ge0}$. Numerical simulation of $(Y_t)_{t\ge0}$ can be done in the following way: Choose an initial ...