Strong solutions for stochastic differential equations with jumps

General stochastic equations with jumps are studied. We provide criteria for the uniqueness and existence of strong solutions under non-Lipschitz conditions of Yamada-Watanabe type. The results are applied to stochastic equations driven by spectrally positive L\'evy processes.Comment: 16 page

Multifractal analysis of superprocesses with stable branching in dimension one

We show that density functions of a $(\alpha,1,\beta)$-superprocesses are almost sure multifractal for $\alpha>\beta+1$, $\beta\in(0,1)$ and calculate the corresponding spectrum of singularities.Comment: Published at http://dx.doi.org/10.1214/14-AOP951 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org