On the Exact Solution of a Generalized Polya Process

Table 2

Some examples of 𝜅(𝑡), and corresponding Λ(𝑡) and exp(Λ(𝑡)).

	𝜅(𝑡)	Λ(𝑡)	𝐹≡exp(Λ(𝑡))	constraint
(i)	𝜅exp(−𝛾𝑡)	𝛼𝜅𝛾(1−exp(−𝛾𝑡))	exp(𝛼𝜅𝛾(1−exp(−𝛾𝑡)))	𝛾>0
(ii)	𝜅1+𝛾𝑡	𝛼𝜅𝛾ln(1+𝛾𝑡)	(1+𝛾𝑡)^𝛼𝜅/𝛾	𝛾>0
(iii)	𝜅𝑡^𝛾−1	𝛼𝜅𝛾𝑡^𝛾	exp(𝛼𝜅𝛾𝑡^𝛾)	0<𝛾<1