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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
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Why does the three points follow by making the two assumptions about the conditioned intensi...
The intensity function is defined as
$$\lambda^*(t)=\frac{f(t|H_{t_n})}{1-F(t|H_{t_n})}$$
where $f$ is the density function and $F$ is the distribution function, and $H_{t_n}$ is the history of all th …