Pathwise estimation of the stochastic functional Kolmogorov-type system

In this paper we stochastically perturb the functional Kolmogorov-type systemx˙(t)=diag(x1(t),…,xn(t))f(xt)into the stochastic functional differential equationdx(t)=diag(x1(t),…,xn(t))[f(xt)dt+g(xt)dw(t)].This paper studies pathwise estimation of the solution to this equation. As the applications, this paper also discusses the pathwise estimation of the solutions of various stochastic Lotka-Volterra-type systems.