Mild solutions of local non-Lipschitz stochastic evolution equations with jumps

By estimating the coefficients functions in the stochastic energy equality, the existence and uniqueness of mild solutions to stochastic evolution equations (SEEs) under local non-Lipschitz condition proposed by Taniguchi with jumps are proved here. The results of Taniguchi (2009) are generalized and improved as a special case of our theory. It should be pointed that the proof for SEEs with jumps is certainly not a straightforward generalization of that for SEEs without jumps and some new techniques are developed to cope with the difficulties due to the Poisson random measures.