ON THE PATHWISE GROWTH RATES OF LARGE FLUCTUATIONS OF STOCHASTIC POPULATION SYSTEMS WITH INFINITE DELAY

In general, time delay and system uncertainty are commonly encountered for all population systems. To examine whether the presence of environmental noise affects infinite delay population systems significantly, this paper perturbs the functional Kolmogorov-type system with infinite delay (x) over dot(t) = diag(x(1)(t), ... , x(n)(t))f(x(t)) into the infinite delay stochastic functional differential system dx(t) = diag(x(1)(t), ... , x(n)(t))[f(x(t))dt + g(x(t))dw(t)]. By the M-matrix technique, this paper examines the global positive solution and its pathwise estimation for this stochastic functional Kolmogorov-type population system. To illustrate the applications of our theory more clearly, this paper also discusses a Lotka-Volterra system with mixed delays as a special case.