On the Exact Solution of a Generalized Polya Process

Table 1

Some typical examples of 𝜆(𝑡) and Λ(𝑡).

	𝜆(𝑡)	⟨𝑛(𝑡)⟩=𝜎^2𝑛(𝑡)=Λ(𝑡)	constraint
(i)	𝜆0exp(−𝛾0𝑡)	𝜆0𝛾0(1−exp(−𝛾0𝑡))	𝛾0>0
(ii)	𝜆01+𝛾0𝑡	𝜆0𝛾0ln(1+𝛾0𝑡)	𝛾0>0
(iii)	𝜆0𝑡^𝛾0−1	𝜆0𝛾0𝑡^𝛾0	0<𝛾0<1