Pathwise estimation of the stochastic functional Kolmogorov-type system

In this paper we stochastically perturb the functional Kolmogorov-type system (t) = diag(x(1)(t), ..., x(n)(t))f(x(t)) into the stochastic functional differential equation dx(t) = diag(x(1)(t), ..., x(n)(t))[f(x(t))dt + g(x(t))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.