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Stochastic integration with respect to a cylindrical special semi-martingale

Year 2022, , 899 - 906, 30.12.2022
https://doi.org/10.31801/cfsuasmas.981876

Abstract

In this research, we introduce the stochastic integration with respect to a cylindrical special semi-martingale, which is a specific case of general integration, with specific properties of special semi-martingales.

References

  • Brzezniak, Z., Van Neerven, J.M.A.M., Stochastic convolution in separable Banach spaces and the stochastic linear Cauchy problem, Studia Math., 143(1) (2000), 43-74.
  • Criens, D., Cylindrical martingale problems associated with Levy generators, J. Theoret. Probab., 32(3) (2019), 1306–1359. https://doi.org/10.48550/arXiv.1706.06049
  • Di Girolami, C., Fabbri, G., Russo, F., The covariation for Banach space valued processes and applications, Metrika, 77(1) (2014), 51-104. https://doi.org/10.48550/arXiv.1301.5715
  • Emery, M., Une Topologie Sur Lespace Des Semimartingales, Sem. Probab. XIII. Univ. Strasbourg, 260–280, Lecture Notes in Math. 721, Springer, 1979.
  • Fonseca-Mora, C.A., Semimartingales on duals of nuclear spaces, Electron. J. Probab., 25(36) (2020). https://doi.org10.1214/20-EJP444
  • Hashemi Sababe, S., Yazdi M., Shabani, M.M., Reproducing kernel Hilbert space based on special integrable semimartingales and stochastic integration, Korean J. Math., 29(3) (2021), 639–647. https://doi.org/10.11568/kjm.2021.29.3.639
  • Jacod, J., Shiryaev, A.N., Limit Theorems for Stochastic Processes, Springer, 2003.
  • Kalinichenko, A.A., An approach to stochastic integration in general separable Banach spaces, Potential Anal., 50(4) (2019), 591–608. https://doi.org/10.1007/s11118-018-9696-4
  • Kalton, N.J., Weis, L.W.,The $H^{\infty}$-calculus and square function estimates, Nigel J. Kalton Selecta, 1 (2016), 715-764. https://doi.org/10.48550/arXiv.1411.0472
  • Kardaras, C., On the closure in the Emery topology of semimartingale wealth-process sets, Ann. Appl. Probab., 23(4) (2013), 1355–1376. http://dx.doi.org/10.1214/12-AAP872
  • Kumar, U., Riedle, M., The stochastic Cauchy problem driven by a cylindrical Levy process, Electron. J. Probab., 25(10), (2020). https://doi.org/10.48550/arXiv.1803.04365
  • Memin, J., Espaces de semimartingales et changement de probabilite, Z. Wahrsch. Verw. Gebiete, 52(1) (1980), 9–39. https://doi.org/10.1007/BF00534184
  • Metivier, M., Pellaumail, J., Stochastic Integration, Probability and Mathematical Statistics, Academic Press, 1980,
  • Mnif, M., Pham, H., Stochastic optimization under constraints, Stochastic Process. Appl., 93 (2001), 149-180. https://doi.org/10.1016/S0304-4149(00)00089-2
  • Ondrejat, M., Brownian representations of cylindrical local martingales, martingale problem and strong Markov property of weak solutions of SPDEs in Banach spaces, Czechoslovak Math. J., 55(130) (2005), 1003–1039. https://doi.org/10.1007/s10587-005-0084-z
  • Rudin, W., Real and Complex Analysis, McGraw-Hill Book Co., 1987.
  • Suchanecki, Z., Weron, A., Decomposability of cylindrical martingales and absolutely summing operators, Math. Z., 185(2) (1984), 271–280. https://doi.org/10.1007/BF01181698
  • Sun, X., Xie, L., Xie, Y., Pathwise uniqueness for a class of SPDEs driven by cylindrical-stable processes, Potential Anal., 53(2) (2020), 659–675. https://doi.org/10.1007/s11118-019-09783-x
  • Veraar, M., Yaroslavtsev, I., Cylindrical continuous martingales and stochastic integration in infinite dimensions, Electron. J. Probab., 21(59) (2016). https://doi.org/10.1214/16-EJP7
Year 2022, , 899 - 906, 30.12.2022
https://doi.org/10.31801/cfsuasmas.981876

Abstract

References

  • Brzezniak, Z., Van Neerven, J.M.A.M., Stochastic convolution in separable Banach spaces and the stochastic linear Cauchy problem, Studia Math., 143(1) (2000), 43-74.
  • Criens, D., Cylindrical martingale problems associated with Levy generators, J. Theoret. Probab., 32(3) (2019), 1306–1359. https://doi.org/10.48550/arXiv.1706.06049
  • Di Girolami, C., Fabbri, G., Russo, F., The covariation for Banach space valued processes and applications, Metrika, 77(1) (2014), 51-104. https://doi.org/10.48550/arXiv.1301.5715
  • Emery, M., Une Topologie Sur Lespace Des Semimartingales, Sem. Probab. XIII. Univ. Strasbourg, 260–280, Lecture Notes in Math. 721, Springer, 1979.
  • Fonseca-Mora, C.A., Semimartingales on duals of nuclear spaces, Electron. J. Probab., 25(36) (2020). https://doi.org10.1214/20-EJP444
  • Hashemi Sababe, S., Yazdi M., Shabani, M.M., Reproducing kernel Hilbert space based on special integrable semimartingales and stochastic integration, Korean J. Math., 29(3) (2021), 639–647. https://doi.org/10.11568/kjm.2021.29.3.639
  • Jacod, J., Shiryaev, A.N., Limit Theorems for Stochastic Processes, Springer, 2003.
  • Kalinichenko, A.A., An approach to stochastic integration in general separable Banach spaces, Potential Anal., 50(4) (2019), 591–608. https://doi.org/10.1007/s11118-018-9696-4
  • Kalton, N.J., Weis, L.W.,The $H^{\infty}$-calculus and square function estimates, Nigel J. Kalton Selecta, 1 (2016), 715-764. https://doi.org/10.48550/arXiv.1411.0472
  • Kardaras, C., On the closure in the Emery topology of semimartingale wealth-process sets, Ann. Appl. Probab., 23(4) (2013), 1355–1376. http://dx.doi.org/10.1214/12-AAP872
  • Kumar, U., Riedle, M., The stochastic Cauchy problem driven by a cylindrical Levy process, Electron. J. Probab., 25(10), (2020). https://doi.org/10.48550/arXiv.1803.04365
  • Memin, J., Espaces de semimartingales et changement de probabilite, Z. Wahrsch. Verw. Gebiete, 52(1) (1980), 9–39. https://doi.org/10.1007/BF00534184
  • Metivier, M., Pellaumail, J., Stochastic Integration, Probability and Mathematical Statistics, Academic Press, 1980,
  • Mnif, M., Pham, H., Stochastic optimization under constraints, Stochastic Process. Appl., 93 (2001), 149-180. https://doi.org/10.1016/S0304-4149(00)00089-2
  • Ondrejat, M., Brownian representations of cylindrical local martingales, martingale problem and strong Markov property of weak solutions of SPDEs in Banach spaces, Czechoslovak Math. J., 55(130) (2005), 1003–1039. https://doi.org/10.1007/s10587-005-0084-z
  • Rudin, W., Real and Complex Analysis, McGraw-Hill Book Co., 1987.
  • Suchanecki, Z., Weron, A., Decomposability of cylindrical martingales and absolutely summing operators, Math. Z., 185(2) (1984), 271–280. https://doi.org/10.1007/BF01181698
  • Sun, X., Xie, L., Xie, Y., Pathwise uniqueness for a class of SPDEs driven by cylindrical-stable processes, Potential Anal., 53(2) (2020), 659–675. https://doi.org/10.1007/s11118-019-09783-x
  • Veraar, M., Yaroslavtsev, I., Cylindrical continuous martingales and stochastic integration in infinite dimensions, Electron. J. Probab., 21(59) (2016). https://doi.org/10.1214/16-EJP7
There are 19 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Articles
Authors

Saeed Hashemi Sababe 0000-0003-1167-5006

Publication Date December 30, 2022
Submission Date August 16, 2021
Acceptance Date April 22, 2022
Published in Issue Year 2022

Cite

APA Hashemi Sababe, S. (2022). Stochastic integration with respect to a cylindrical special semi-martingale. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(4), 899-906. https://doi.org/10.31801/cfsuasmas.981876
AMA Hashemi Sababe S. Stochastic integration with respect to a cylindrical special semi-martingale. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2022;71(4):899-906. doi:10.31801/cfsuasmas.981876
Chicago Hashemi Sababe, Saeed. “Stochastic Integration With Respect to a Cylindrical Special Semi-Martingale”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 4 (December 2022): 899-906. https://doi.org/10.31801/cfsuasmas.981876.
EndNote Hashemi Sababe S (December 1, 2022) Stochastic integration with respect to a cylindrical special semi-martingale. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 4 899–906.
IEEE S. Hashemi Sababe, “Stochastic integration with respect to a cylindrical special semi-martingale”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 4, pp. 899–906, 2022, doi: 10.31801/cfsuasmas.981876.
ISNAD Hashemi Sababe, Saeed. “Stochastic Integration With Respect to a Cylindrical Special Semi-Martingale”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/4 (December 2022), 899-906. https://doi.org/10.31801/cfsuasmas.981876.
JAMA Hashemi Sababe S. Stochastic integration with respect to a cylindrical special semi-martingale. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:899–906.
MLA Hashemi Sababe, Saeed. “Stochastic Integration With Respect to a Cylindrical Special Semi-Martingale”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 4, 2022, pp. 899-06, doi:10.31801/cfsuasmas.981876.
Vancouver Hashemi Sababe S. Stochastic integration with respect to a cylindrical special semi-martingale. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(4):899-906.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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