Time factorization of the higher-order intensity correlation functions in the theory of resonance fluorescence

The intensity correlation functions $Tr{{ρ}(0){s}⁺(t){s}⁺(t+{{τ}}₁){⋯}{s}⁺(t+{{Σ}}ᵢ₌₁ⁿ{{τ}}ᵢ){s}^{{-}}(t+{{Σ}}ᵢ₌₁ⁿ{{τ}}ᵢ){⋯}{s}^{{-}}(t+{{τ}}₁){s}^{{-}}(t)}$ associated with a two-level atom undergoing Markovian dynamics [${s}^{±{}}(t)being the spin- operators for the atom] are shown to factorize in the formf(t){{Π}}ᵢ₌₁ⁿg({{τ}}ᵢ)$ with $f(t)$ [$g(t)$] giving the probability of finding the atom in the excited state when initially it is in the state ${ρ}(0)$ [ground state].