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Mat. Sb. (N.S.), 1980, Volume 111(153), Number 2, Pages 293–307 (Mi msb2593)  

This article is cited in 1 scientific paper (total in 1 paper)

On the representation of integral-valued random measures and local martingales by means of random measures with deterministic compensators

Yu. M. Kabanov, R. Sh. Liptser, A. N. Shiryaev


Abstract: 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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English version:
Mathematics of the USSR-Sbornik, 1981, 39:2, 267–280

Bibliographic databases:

UDC: 519.2
MSC: 60G57, 60G44
Received: 11.01.1979

Citation: 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”, Mat. Sb. (N.S.), 111(153):2 (1980), 293–307; Math. USSR-Sb., 39:2 (1981), 267–280

Citation in format AMSBIB
\Bibitem{KabLipShi80}
\by Yu.~M.~Kabanov, R.~Sh.~Liptser, A.~N.~Shiryaev
\paper On the representation of integral-valued random measures and local martingales by means of random measures with deterministic compensators
\jour Mat. Sb. (N.S.)
\yr 1980
\vol 111(153)
\issue 2
\pages 293--307
\mathnet{http://mi.mathnet.ru/msb2593}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=564354}
\zmath{https://zbmath.org/?q=an:0462.60054|0427.60050}
\transl
\jour Math. USSR-Sb.
\yr 1981
\vol 39
\issue 2
\pages 267--280
\crossref{https://doi.org/10.1070/SM1981v039n02ABEH001515}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MK40500008}


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    This publication is cited in the following articles:
    1. Theory Probab. Appl., 48:1 (2004), 181–188  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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