Set-Valued Stochastic Integrals with Respect to Finite Variation Processes

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References

[1] M. Kisielewicz, “Set-Valued Stochastic Integrals and Stochastic Inclusions,” Discussiones Mathematicae, Vol. 13, 1993, pp. 119-126.

[2] B. K. Kim and J. H. Kim, “Stochastic Integrals of Set-Valued Processes and Fuzzy Processes,” Journal of Mathematical Analysis and Applications, Vol. 236, No. 2, 1999, pp. 480-502.

http://dx.doi.org/10.1006/jmaa.1999.6461

[3] R. J. Aumann, “Intgrals of Set-Valued Functions,” Journal of Mathematical Analysis Applications, Vol. 12, No. 1, 1965, pp. 1-12.

http://dx.doi.org/10.1016/0022-247X(65)90049-1

[4] E. J. Jung and J. H. Kim, “On Set-Valued Stochastic Integrals,” Stochastic Analysis and Applications, Vol. 21, No. 2, 2003, pp. 401-408.

http://dx.doi.org/10.1081/SAP-120019292

[5] S. Li and A. Ren, “Representation Theorems, Set-Valued and Fuzzy Set-Valued Ito Integral,” Fuzzy Sets and Systems, Vol. 158, No. 9, 2007, pp. 949-962.

http://dx.doi.org/10.1016/j.fss.2006.12.004

[6] J. Zhang, “Set-Valued Stochastic Integrals with Respect to a Real Valued Maringale,” Soft Method for Handling Vaelability and Imprecision ASC 48, Spinger-Verlag, Berlin Herdelberg, 2008.

[7] J. Zhang, S. Li, I. Mitoma and Y. Okazaki, “On Set-Valued Stochastic Integrals in M-Type 2 Banach Space,” Journal of Mathematical Analysis and Applications, Vol. 350, No. 1, 2009, pp. 216-233.

http://dx.doi.org/10.1016/j.jmaa.2008.09.017

[8] J. Zhang, S. Li, I. Mitoma and Y. Okazaki, “On the Solution of Set-Valued Stochastic Differential Equations in M-Type 2 Banach Space,” Tohoku Mathematical Journal, Vol. 61, No. 3, 2009, pp. 417-440.

http://dx.doi.org/10.2748/tmj/1255700202

[9] J. Zhang, “Integrals and Stochastic Differential Equations for Set-Valued Stochastic Processes,” Ph.D. Thesis, Saga University, Saga, 2009.

[10] I. Mitoma, Y. Okazaki and J. Zhang, “Set-Valued Stochastic Differential Equations in M-Type 2 Banach Space,” Communications on Stochastic Analysis, Vol. 4, No. 2, 2010, pp. 215-237.

[11] J. G. Li, S. Li and Y. Ogura, “Strong Solutions of Ito Type Set-Valued Stochastic Differential Equation,” Acta Mathematica Sinica, English Series, Vol. 26, No. 9, 2010, pp. 1739-1748.

http://dx.doi.org/10.1007/s10114-010-8298-x

[12] M. Malinowski and M. Michta, “Set-Valued Stochastic Integral Equations Driven by Martingales,” Journal of Mathematical Analysis and Applications, Vol. 394, No. 12, 2012, pp. 30-47.

http://dx.doi.org/10.1016/j.jmaa.2012.04.042

[13] J. Zhang, I. Mitoma and Y. Okazaki, “Set-Valued Stochastic Integrals with Respect to Poisson Processes in a Banach Space,” International Journal of Approximate Reasoning, Vol. 54, No. 3, 2013, pp. 404-417.

http://dx.doi.org/10.1016/j.ijar.2012.06.001

[14] Z. Wang and R. Wang, “Set-Valued Lebesgue-Stieltjes Integrals,” Journal of Applied Probability and Statistics, Vol. 13, No. 3, 1997, pp. 303-316.

[15] S. Li, Y. Ogura and Y. Kreinovich, “Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables,” 43rd Edition, Kluwer Academic Publishers, Dordrecht, 2002.

http://dx.doi.org/10.1007/978-94-015-9932-0

[16] W. Zhang, S. Li, Z. Wang and Y. Gao, “An Introduction about Set-Valued Stochastic Process,” Science Press, Beijing, 2007.

[17] L. Wang and H. Xue, “Set-Valued Lebesgue-Stieltjes Integrals,” Basic Sciences Journal of Textile Universities, Vol. 16, No. 4, 2004, pp. 317-320.