On the Exact Solution of a Generalized Polya Process

Table 3

Summary of the generalized Polya and non-stationary Yule-Furrey process.

Parameters	𝑃(𝜃)	⟨𝑛(𝑡)⟩	𝑉(𝑡)	𝐹
(i) 𝛼≠0,𝛽≠0,𝑛0=0	(𝑛^𝑛+𝑟+1)𝜃^𝑟(1−𝜃)^𝑛	𝑟(𝜃^−1−1)	𝑟𝜃^−1(𝜃^−1−1)	𝐹>1
(ii) 𝛼≠0,𝛽=0,𝑛0=1	𝜃(1−𝜃)^𝑛−1	𝜃^−1	𝜃^−1(𝜃^−1−1)	𝐹>0