where κ κ m is the m th cumulant of x . The first two cumulants are related to the first two moments, μ μ , via κ κ 1 = μ μ 1 ; and κ κ 2 = μ μ 2 − − μ μ 1 2 , where the second cumulant is the so-called variance, σ σ 2 . With these definitions accounted for one can investigate the moments of the Brownian particle PDF,