In this paper we investigate a stochastic model for an economic game. To
describe this model we have used a Wiener process, as the noise has a
stabilization effect. The dynamics are studied in terms of stochastic stability
in the stationary state, by constructing the Lyapunov exponent, depending on
the parameters that describe the model. Also, the Lyapunov function is
determined in order to analyze the mean square stability. The numerical
simulation that we did justifies the theoretical results.
In this paper we established the condition for a curve to satisfy stochastic
generalized fractional HP (Hamilton-Pontryagin) equations. These equations are
described using Ito integral. We have also considered the case of stochastic
generalized fractional Hamiltonian equations, for a hyperregular Lagrange
function. From the stochastic generalized fractional Hamiltonian equations,
Langevin generalized fractional equations were found and numerical simulations
were done.