Stochastic integrals of point processes and the decomposition of two- parameter martingales
Let M be a two-parameter square-integrable martingale with trajectories that have limits in all quadrants and are continuous from the right. The paper gives the decomposition of M into four orthogonal components: \(M=\sum^{4}_{i=1}M_ i,\) where \(M_ 1\) is continuous, \(M_ 2\) is purely discontinuous, \(M_ 3\) and \(M_ 4\) are continuous in one coordinate and purely discontinuous in the other coordinate. \(M_ 2\), \(M_ 3\) and \(M_ 4\) are represented as stochastic integrals with some point measures as integrators.
scientific article; zbMATH DE number 4117565
scientific article