Cramer's theorem for nonnegative multivariate point processes with   independent increments
  We consider a continuous time version of Cramer's theorem with nonnegative summands $ S_t=\frac{1}{t}\sum_{i:\tau_i\le t}\xi_i, t \to\infty, $ where $(\tau_i,\xi_i)_{i\ge 1}$ is a sequence of random variables such that $tS_t$ is a random process with independent increments. 
F. Klebaner, R. Liptser