the Cox process

Several have asked me about the Cox process mentioned on P3 of the paper. I have written a short summary (see attachment). The time of default definition looks a little strange but it is convenient to define it like this, introducing an exponential random variable, because of the subsequent calculations. It could have been defined in terms of a Cox process.

As you may have gathered from studying the paper, there are three main parts in pages 1-12.

Proposition 1.3, whose proof is largely self-contained.

Proposition 1.6 which relies mainly on reference [9]

Theorem 1.9 whose proof involves material from various references.”
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