92 research outputs found
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
Skew convolution semigroups and affine Markov processes
A general affine Markov semigroup is formulated as the convolution of a
homogeneous one with a skew convolution semigroup. We provide some sufficient
conditions for the regularities of the homogeneous affine semigroup and the
skew convolution semigroup. The corresponding affine Markov process is
constructed as the strong solution of a system of stochastic equations with
non-Lipschitz coefficients and Poisson-type integrals over some random sets.
Based on this characterization, it is proved that the affine process arises
naturally in a limit theorem for the difference of a pair of reactant processes
in a catalytic branching system with immigration.Comment: Published at http://dx.doi.org/10.1214/009117905000000747 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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