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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] K. Dellasheri, Emkosti i sluchainye protsessy, izd-vo “Mir”, Moskva, 1975 | MR

[2] J. Jacod, “Multivariate point processes: predictable projection, Radon–Nikodym derivatives, representation of martingales”, Z. W-theorie, 31 (1975), 235–253 | MR | Zbl

[3] Yu. M. Kabanov, R. Sh. Liptser, A. N. Shiryaev, “Absolyutnaya nepreryvnost i singulyarnost lokalno absolyutno nepreryvnykh veroyatnostnykh raspredelenii. I”, Matem. sb., 107(149) (1978), 364–415 | MR | Zbl

[4] A. V. Skorokhod, Issledovaniya po teorii sluchainykh protsessov, izd-vo KGU, Kiev, 1961

[5] B. I. Grigelionis, “O predstavlenii tselochislennykh sluchainykh mer kak stokhasticheskikh integralov po puassonovskoi mere”, Lit. matem. sb., XI:1 (1971), 93–108 | MR

[6] N. El Karoui, J.-P. Lepeltier, “Représentation des processus ponctuels multivariés à l'aide l'un processus de Poisson”, Z. W-theorie, 39 (1977), 111–133 | MR | Zbl

[7] H. Tanaka, “On the uniqueness of Markov process associated with the Boltzmann equation of Maxwellian molecules”, Proc. of the Intern. Symposium on Stochostic Differential Equation (Kyoto, Japan, 1976), Tokyo, Japan, 1978 | MR

[8] P. A. Meyer, “Un Cours sur les intégrates stochastique”, Lecture Notes Math., 511 (1976), 245–400 | DOI | MR | Zbl

[9] Dzh. L. Dub, Veroyatnostnye protsessy, IL, Moskva, 1956

[10] J. Jacod, J. Memin, “Caracteristiques locales et condition de continuité absolue pour les semimartingales”, Z. W-theorie, 35 (1976), 1–37 | MR | Zbl

[11] B. I. Grigelionis, “O martingalnoi kharakterizatsii sluchainykh protsessov s nezavisimymi prirascheniyami”, Lit. matem. sb., XVII:1 (1977), 75–86 | MR

[12] R. K. Getoor, “Sur la construction de noyaux”, Lecture Notes Math., 465 (1975), 443–463 | DOI | MR | Zbl

[13] P. A. Meier, Veroyatnost i potentsialy, izd-vo “Mir”, Moskva, 1973

[14] A. V. Skorokhod, “Ob odnom predstavlenii sluchainykh velichin”, Teoriya veroyatn., XXI:3 (1976), 645–648

[15] C. Dellacherie, P.-A. Meyer, Probabilités et potentiel, Hermann, Paris, 1975 | MR | Zbl

[16] P. Sh. Liptser, A. N. Shiryaev, Statistika sluchainykh protsessov, izd-vo “Nauka”, Moskva, 1974 | MR