On asymptotic behaviour of probabilities of large deviations for compound Cox processes

We derive logarithmic asymptotics for probabilities of large deviations for compound Cox processes. We show that under appropriate conditions, these asymptotics are the same as those for sums of independent random variables and processes with independent increments. When these conditions do not hold, the asymptotics of large deviations probabilities for compound Cox processes are quite different. Bibl. – 5 titles.