This work is devoted to the travelling wave solutions and asymptotic speed for a two-species stochastic competitive system driven by multiplicative Itô type white noise. By introduction of sup-solutions sub-solutions, existence approximations are proven under some conditions on parameters. Moreover, combining with Feynman-Kac formula, sub-solution, sup-solution, monotone iteration equilibria ki...

We study the optimal control problem for a weighted mean-field system. A new feature of is that coefficients depend on state process as well its measure and variable. By applying variational technique, we establish stochastic maximum principle. Also, sufficient condition optimality. As an application, investigate premium policy insurance firm asset–liability management problem.

Along with the progress of science and technology development social civilization, control system brings an increasingly significant function in daily life. The application field is very wide, for instance, mobile [1], artificial earth satellite [2], pest [3], etc.