On the Exact Solution of a Generalized Polya Process

Figure 4

Time dependence of 𝑝(𝑛,𝑡) in (3.15) for three relaxation functions for 𝜅(𝑡) in Table 2: (i) an exponential function, and (ii) an inverse power function, (iii) a fractional power function; the values of parameters are 𝛼=1, 𝜅=1, and 𝛾=0.85. The pdf profiles are depicted for 𝑡=0.4 (solid line), 𝑡=1.2 (dotted line), 𝑡=2.0 (dashed line), 𝑡=2.8 (dash-dotted line) and 𝑡=3.6 (dash-dotted line).