Geodesic
Stochastic equations with discontinuous jump functions
Matematičeskie trudy, Tome 20 (2017) no. 1, pp. 128-144

Voir la notice de l'article provenant de la source Math-Net.Ru

In the present article, we consider a stochastic differential equation that contains an integral with respect to a Poisson measure but avoids the diffusion term. The integrand need not be continuous. We introduce a definition of a solution and prove the existence and uniqueness theorems. 
@article{MT_2017_20_1_a7,
     author = {A. V. Logachov and S. Ya. Makhno},
     title = {Stochastic equations with discontinuous jump functions},
     journal = {Matemati\v{c}eskie trudy},
     pages = {128--144},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2017_20_1_a7/}
}
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A. V. Logachov; S. Ya. Makhno. Stochastic equations with discontinuous jump functions. Matematičeskie trudy, Tome 20 (2017) no. 1, pp. 128-144. http://geodesic.mathdoc.fr/item/MT_2017_20_1_a7/