Soren Tolver Jensen and Bent Nielsen
  (1997)
  'On convergence of multivariate Laplace transforms'
  Statistics and Probability Letters 33, p 125-128.

  ABSTRACT:

  It is well-known that convergence of Laplace transforms in a
  neighbourhood of the origin is a sufficient criteria for weak
  convergence. It is worthwhile to note that the interior of the
  set of convergence porints is convex. This provides a link to
  exponential family theory. As an example an autoregressive
  model is studied.