THE ITO AND STRATONOVICH INTEGRALS FOR STOCHASTIC DIFFERENTIAL-EQUATIONS WITH POISSON WHITE-NOISE

The relationship between the Ito and the Stratonovich integrals used f or solving stochastic differential equations with Gaussian white noise is well known. However, this relationship seems to be less clear when dealing with stochastic differential equations driven by Poisson whit e noise. It is shown that there is no difference between the Ito and t he Stratonovich integrals used to define the solution of stochastic di fferential equations with Poisson white noise. This result is in disag reement with findings of some previous publications but in agreement w ith the classical definition of the Ita and Stratonovich integrals. In tuitive considerations, arguments based on the theory of stochastic in tegrals with semimartingales, and examples are used to prove and demon strate the claimed equality of the Ito and Stratonovich integrals. (C) 1998 Elsevier Science Limited.