A satellite circles a body in outer space and records a special feature of the body (e.g. rocks, water, low elevations) along a path it monitors. As an idealized model, assume the feature occurs on...

A satellite circles a body in outer space and records a special feature of the body (e.g. rocks, water, low elevations) along a path it monitors. As an idealized model, assume the feature occurs on the polar-angle space S = [0, 2π] at angles Θ₁
≤ Θ₂
... ≤ 2π that form a Poisson process with intensity μ. We will only consider one orbit of the satellite. Suppose the satellite is moving at a (deterministic) velocity of γ radians per unit time. Upon observing an occurrence at Θ_n
the satellite sends a message to a station that receives it after a time τn. Suppose the transmission times τn are independent with distribution G and are independent of the positions of the occurrences. Consider the point process M on S × R²
₊, where M((α, β] × (a, b] × (c, d]) is the number of occurrences in the radian set (α, β] that are observed in the time set (a, b] and received at the station in the time set (c, d]. Describe the process M and its intensity measure in terms of the system data. Next, let N(t) denote the number of messages received at the station in (0, t] whose transmission time exceeds a certain limit L, where G(L) <>