conditional law g(t) for negative t

[kakarun]

Hi,

I follow the method in "Estimation of slowly decreasing Hawkes kernels: application to high-frequency order book dynamics" to solve Wiener-Hopf systems for multidimensional hawkes process.

I was wondering how to determine the value for g_ij(t) when t is negative.

Is that true g_ij(t) = g_ij(-t)*Lambda^i/Lambda^j for t < 0?

Thanks!