ON ASYMPTOTIC BEHAVIOUR OF PROBABILITIES OF SMALL DEVIATIONS FOR COMPOUND COX PROCESSES

ANDREI N. FROLOV
Theory of Stochastic Processes Vol. 14 (30), no. 2, 2008, pp. 19–27
We derive logarithmic asymtotics for probabilities of small deviations for compound Cox processes in the space of trajectories. We find conditions under which these asymptotics are the same as those for sums of independent identically distributed random variables and homogeneous processes with independent increments. We show that if these conditions do not hold, the asymptotics of small deviations for compound Cox processes are quite different.


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