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On pathwise stochastic integration

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  • Karandikar, Rajeeva L.
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    Abstract

    In this article, we construct a mapping : D[0, [infinity])xD[0,[infinity])-->D[0,[infinity]) such that if (Xt) is a semimartingale on a probability space ([Omega], , P) with respect to a filtration (t) and if (ft) is an r.c.l.l. (t) adapted process, then This is of significance when using stochastic integrals in statistical inference problems. Similar results on solutions to SDEs are also given.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 57 (1995)
    Issue (Month): 1 (May)
    Pages: 11-18

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    Handle: RePEc:eee:spapps:v:57:y:1995:i:1:p:11-18

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    Related research

    Keywords: Brownian motion Semimartingale Stochastic integral;

    References

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    1. Karandikar, Rajeeva L., 1983. "Stochastic integration w.r.t. continuous local martingales," Stochastic Processes and their Applications, Elsevier, vol. 15(2), pages 203-209, July.
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    Citations

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    Cited by:
    1. Bhatt, Abhay G. & Karandikar, Rajeeva L., 2002. "Robustness of the nonlinear filter: the correlated case," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 41-58, January.
    2. Nicolas Perkowski & David J. Pr\"omel, 2013. "Pathwise stochastic integrals for model free finance," Papers 1311.6187, arXiv.org.
    3. Larry Epstein & Shaolin Ji, 2011. "Ambiguous Volatility, Possibility and Utility in Continuous Time," Papers 1103.1652, arXiv.org, revised Jan 2013.
    4. A. Galichon & P. Henry-Labord\`ere & N. Touzi, 2014. "A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options," Papers 1401.3921, arXiv.org.
    5. Masaaki Fukasawa, 2014. "Efficient discretization of stochastic integrals," Finance and Stochastics, Springer, vol. 18(1), pages 175-208, January.
    6. Budhiraja, A., 2001. "Ergodic properties of the nonlinear filter," Stochastic Processes and their Applications, Elsevier, vol. 95(1), pages 1-24, September.
    7. Masaaki Fukasawa, 2012. "Efficient Discretization of Stochastic Integrals," Papers 1204.0637, arXiv.org.
    8. Erhan Bayraktar & Song Yao, 2013. "On the Robust Optimal Stopping Problem," Papers 1301.0091, arXiv.org, revised Jul 2014.
    9. Marcel Nutz, 2014. "Robust Superhedging with Jumps and Diffusion," Papers 1407.1674, arXiv.org.
    10. B. Acciaio & M. Beiglb\"ock & F. Penkner & W. Schachermayer & J. Temme, 2012. "A trajectorial interpretation of Doob's martingale inequalities," Papers 1202.0447, arXiv.org, revised Jul 2013.

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