Section 4: The UMTS Forum in .NET
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X(t) represents the number of births in the time interval (0, t]. The word births is used quite generally. Historically, such a process was used to model the population growth of certain organisms under steadystate conditions such as no mortality or immigration. In analysis of stochastic processes, the standard approach is to solve conditions 2 and 3 as differential equations for h small. The rst condition is a boundary condition and the last condition merely ensures that there are no deaths (i.e., the process is continually growing). This is why the process is also sometimes referred to as a rightshift process. Letting Pn (t) = P [X(t) = n], the differential equations that must be solved are P0 (t) = 0 P0 (t) Pn (t) = n Pn (t) + n 1 Pn 1 (t) for n 1. (7.3)

