Restricted Gompertz-Type Diffusion Processes with Periodic Regulation Functions

Virginia Giorno, Amelia G. Nobile
2019 Mathematics  
We consider two different time-inhomogeneous diffusion processes useful to model the evolution of a population in a random environment. The first is a Gompertz-type diffusion process with time-dependent growth intensity, carrying capacity and noise intensity, whose conditional median coincides with the deterministic solution. The second is a shifted-restricted Gompertz-type diffusion process with a reflecting condition in zero state and with time-dependent regulation functions. For both
more » ... s, we analyze the transient and the asymptotic behavior of the transition probability density functions and their conditional moments. Particular attention is dedicated to the first-passage time, by deriving some closed form for its density through special boundaries. Finally, special cases of periodic regulation functions are discussed.
doi:10.3390/math7060555 fatcat:xqozu5fk5vbhrhf5sm2sv4l7c4