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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 as

$$\lambda_tdt=P(N_t \text{ jumps in } [t,t+dt]\vert \mathcal{F}_t).$$

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    $\begingroup$ You can try looking for older literature on point processes (more recently point processes mostly mean random point fields), see if this helps $\endgroup$
    – Leonid Petrov
    Commented Nov 27, 2016 at 14:59

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