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Teor. Veroyatnost. i Primenen., 1972, Volume 17, Issue 4, Pages 761–765 (Mi tvp4352)  

This article is cited in 9 scientific papers (total in 9 papers)

Short Communications

On an identity for stochastic integrals

A. A. Novikov

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: A sufficient condition is obtained for the identity
$$ \mathbf{M}\exp\{\int_0^T f(t,\omega) dw(t)-\frac12\int_0^T f^2(t,\omega) dt\}=1 $$
to hold. (Here $\int_0^T f(t,\omega) dw(t)$ is the stochastic integral with respect to a Wiener process $w(t)$.) This condition is shown to be close to a necessary one.

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English version:
Theory of Probability and its Applications, 1973, 17:4, 717–720

Bibliographic databases:

Received: 25.10.1971

Citation: A. A. Novikov, “On an identity for stochastic integrals”, Teor. Veroyatnost. i Primenen., 17:4 (1972), 761–765; Theory Probab. Appl., 17:4 (1973), 717–720

Citation in format AMSBIB
\Bibitem{Nov72}
\by A.~A.~Novikov
\paper On an identity for stochastic integrals
\jour Teor. Veroyatnost. i Primenen.
\yr 1972
\vol 17
\issue 4
\pages 761--765
\mathnet{http://mi.mathnet.ru/tvp4352}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=312567}
\zmath{https://zbmath.org/?q=an:0284.60054}
\transl
\jour Theory Probab. Appl.
\yr 1973
\vol 17
\issue 4
\pages 717--720
\crossref{https://doi.org/10.1137/1117088}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Novikov, “On conditions for absolute continuity of probability measures”, Math. USSR-Sb., 35:5 (1979), 697–707  mathnet  crossref  mathscinet  zmath  isi
    2. Kallsen J., Shiryaev A., “The Cumulant Process and Esscher's Change of Measure”, Financ. Stoch., 6:4 (2002), 397–428  crossref  isi
    3. A. N. Shiryaev, “O martingalnykh metodakh v zadachakh o peresechenii granits brounovskim dvizheniem”, Sovr. probl. matem., 8, MIAN, M., 2007, 3–78  mathnet  crossref  zmath
    4. Hulley H., Platen E., “A Visual Criterion for Identifying Ito Diffusions as Martingales or Strict Local Martingales”, Seminar on Stochastic Analysis, Random Fields and Applications, Progress in Probability, 63, 2011, 147–157  isi
    5. Mijatovic A., Urusov M., “On the martingale property of certain local martingales”, Probab Theory Related Fields, 152:1–2 (2012), 1–30  crossref  isi
    6. Sokol A. Hansen N.R., “Exponential Martingales and Changes of Measure For Counting Processes”, Stoch. Anal. Appl., 33:5 (2015), 823–843  crossref  isi
    7. Bernard C. Cui Zh. McLeish D., “on the Martingale Property in Stochastic Volatility Models Based on Time-Homogeneous Diffusions”, Math. Financ., 27:1 (2017), 194–223  crossref  mathscinet  zmath  isi  scopus
    8. Hulley H., Ruf J., “Weak Tail Conditions For Local Martingales”, Ann. Probab., 47:3 (2019), 1811–1825  crossref  mathscinet  isi  scopus
    9. B. Chiqvinidze, “New proof of the Novikov criterion using backward stochastic differential equations”, Theory Stoch. Process., 24(40):2 (2019), 14–16  mathnet
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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