Geodesic
On the representation of integral-valued random measures and local martingales by means of random measures with deterministic compensators
Sbornik. Mathematics, Tome 39 (1981) no. 2, pp. 267-280

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The relation $\mu(\omega;A)=p(\omega;\psi^{-1}_\omega(A))$ between integral-valued measures $\mu(\omega;\cdot\,)$ and $p(\omega;\cdot\,)$ and the compensators $\nu(\omega;\cdot\,)$ and $q(\,\cdot\,)$, respectively, is established ($q$ is a deterministic measure), where $\psi_\omega(\,\cdot\,)$ is a predictable mapping, provided that $\nu(\omega;A)=q(\psi^{-1}_\omega(A))$. This result is used to represent a local martingale in the form of a sum of stochastic integrals with respect to a continuous Gaussian martingale and the martingale measure $p-q$. Bibliography: 16 titles. 
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     author = {Yu. M. Kabanov and R. Sh. Liptser and A. N. Shiryaev},
     title = {On the representation of integral-valued random measures and local martingales by means of random measures with deterministic compensators},
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Yu. M. Kabanov; R. Sh. Liptser; A. N. Shiryaev. On the representation of integral-valued random measures and local martingales by means of random measures with deterministic compensators. Sbornik. Mathematics, Tome 39 (1981) no. 2, pp. 267-280. http://geodesic.mathdoc.fr/item/SM_1981_39_2_a7/