Speaker
Description
We present an inverse problem related to the dynamics of an age-structured population in which the evolution of individuals is also influenced by some random events. The model consists in a stochastic equation describing the time and age evolution of a population, governed by vital factors and influenced by a linear multiplicative noise perturbation, possibly related to emigration, immigration, environmental particularities, climate influence, epidemics, catastrophes, food availability at a given time and fortuitous mortality. A minimization problem is associated to this system, with the goal of identifying the mortality rate and the coefficient in the stochastic term, analogous to the volatility, by knowing the total population at certain times. A rescaling formula transforms the state system in a deterministic differential one with random coefficients. After proving existence and uniqueness results for this state system and the existence of a least one solution to the minimization problem, the inverse problem is solved by following an optimal control technique, proving the necessary conditions of optimality, that is the expressions of the two parameters which ensure the achievement of the objective.