We analyze some widespread models of population dynamics (logistic , \theta-logistic , and Gompertz model). In the first part of the article we discuss the deterministic versions of these models . The discussion is also instrumental , on the basis of some very simplified , but working, hypotheses , to frame the logistic and \theta-logistic equations in an unified context, within which also the Gompertz model emerges from  anomalous scaling. In the second half of the paper we pass then to deal with the logistic and \theta-logistic stochastic models for which, but for the Gompertz case, many aspects are not completely defined. The solutions of the processes contain in fact some exponential functionals of Brownian motion, a rather complex kind of processes extensively studied in financial contexts. First, we recall a few known results, and then we exploit some integral representation that allow to establish simple estimates on the moments of the processes. Furthermore, we derive closed expressions for the transition probability density functions, on which too we obtain some easy estimate implying other bounds for all the moments
In the present paper we provide the closed form of the path-like solutions for the logistic and \theta-logistic stochastic differential equations, along with the exact expressions of both their probability density functions and their moments. We simulate in addition a few typical sample trajectories, and we provide a few examples of numerical computation of the said closed formulas at different noise intensities: this shows in particular that an increasing randomness - while making the process more unpredictable - asymptotically tends to suppress in average the logistic growth. These main results are preceded by a discussion of the noiseless, deterministic versions of these models : a prologue which turns out to be instrumental - on the basis of a few simplified but functional hypotheses - to frame the logistic and \theta-logistic equations in a unified context, within which also the Gompertz model emerges from an anomalous scaling. 
R
We analyze some widespread models of population dynamics (logistic ,
In the present paper we provide the closed form of the path-like solutions for the logistic and
R
, and Gompertz model). In the first part of the article we discuss the
stochastic differential equations, along with the exact expressions of both their probability density functions and their moments. We simulate in addition a few typical sample trajectories, and we provide a few examples of numerical computation of the said closed formulas at different noise intensities: this shows in particular that an increasing randomness - while making the process more unpredictable - asymptotically tends to suppress in average the logistic growth. These main results are preceded by a discussion of the noiseless,
R
. The discussion is also instrumental ,
: a prologue which turns out to be instrumental -
R
some very simplified , but working, hypotheses ,
a few simplified but functional hypotheses -
R
an
a
A
an
D
In the second half of the paper we pass then to deal with the logistic and \theta-logistic stochastic models for which, but for the Gompertz case, many aspects are not completely defined. The solutions of the processes contain in fact some exponential functionals of Brownian motion, a rather complex kind of processes extensively studied in financial contexts. First, we recall a few known results, and then we exploit some integral representation that allow to establish simple estimates on the moments of the processes. Furthermore, we derive closed expressions for the transition probability density functions, on which too we obtain some easy estimate implying other bounds for all the moments