Abstract
By means of Riemann-Stieltjes stochastic process, moment-generating functions and operator-Valued mathematical expectation,the problem of probabilistic approximation for bi-continuous semigroups was studied and the general probabilistic approximation of exponential formulas and the generation theorems were given.
Supported by the fundamental research funds for the central universities (JCB1201B).
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References
Kuhnemund: A hille-yosida theorem for bi-continuous semigroups. J. Semigroup Forum 67(2), 205–225 (2003)
Albanese, A., Mangino, E.: Trotter-Kato theorems for bi-continuous semigroups and applications to Feller semigroups. J. Math. Anal. Appl. 289, 477–492 (2003)
Khnemund, F., van Neerven, J.: A Lie-Trotter product formula for Ornstein-Uhlenbeck semigroups in infinite dimensions. J. Evol. Equ. 4, 53–73 (2004)
Jara, P.: Rational approximation schemes for bi-continuous semigroups. Journal of Mathematical Analysis and Applications 344, 956–968 (2008)
Pfeifer, D.: Approximation-theoretic aspects of probabilistic representations for operator semigroups. Journal of Approximation Theory 43(3), 271–296 (1985)
Pfeifer, D.: Probabilistic concepts of approximation theory in connection with operation semigroups. J. Approximation Theory and Its Applications 1(4), 93–118 (1985)
Pfeifer, D., Burter, P.L.: Some general probabilistic estimations for the rate of convergence in operator semigroup representations. Applicable Analysis 23, 111–118 (1985)
Chen, W.-Z.: A representation formula of C infinitesimal generator. Journal of Xiamen University: Nature Science 32(2), 135–140 (1993)
Chen, W.-Z.: Saturation theorem of probabilistic representation formulas of C-semigroups. Journal of Xiamen University: Nature Science 34(1), 1–6 (1995)
Song, X.-Q., Peng, A.-M.: Probabilistic approximation for C-semigroup and integrated semigroups. Journal of Nanjing University: Mathematical Biquarterly 20(2), 216–225 (2003)
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Cang, D., Ge, S. (2012). Approximation Theoretic Aspects of Probabilistic Representations for Bi-continuous Semigroups. In: Liu, C., Wang, L., Yang, A. (eds) Information Computing and Applications. ICICA 2012. Communications in Computer and Information Science, vol 308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34041-3_48
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DOI: https://doi.org/10.1007/978-3-642-34041-3_48
Publisher Name: Springer, Berlin, Heidelberg
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