An alternative expression for stochastic dynamical systems with parametric Poisson white noise

Di Paola and Falsone's formula is widely used in expressing a correction term to the usual Ito integral in stochastic dynamical systems with parametric Poisson white noise. An alternative expression is presented here. Comparing with Di Paola and Falsone's original expression, the alternative one is applicable under more general conditions, and shows significantly improved performance in numerical implementation. The alternative expression turns out to be a special case of the Marcus integrals.

► Give an alternative expression of Di Paola and Falsone's formula.
► The alternative expression can be applied under more general condition.
► The alternative expression shows advantages in many applications.