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- W1972071232 abstract "By the Dambis--Dubins--Schwarz theorem, any stochastic integral $M:=int_0^cdot H_sdW_s$ of Brownian motion can be written as a time-changed Brownian motion, i.e., $M=({widehat{W}}_{widehat{T_t}})_{tinbf{R}_+}$ for some Brownian motion $({widehat{W}}_theta)_{thetainbf{R}_+}$ and some time change $({widehat{T_t}})_{tinbf{R}_+}$. In [J. Jacod and A. Shiryaev, Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin--Heidelberg, 1987] and [O. Kallenberg, Stochastic Process. Appl., 40 (1992), pp.~199--223] it is shown that in this statement Brownian motion can be replaced with (symmetric) $alpha$-stable Levy motion}. Using the cumulant process of a semimartingale, we give new short proofs. Moreover, we show that the statement cannot be extended to any other Levy processes." @default.
- W1972071232 created "2016-06-24" @default.
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- W1972071232 date "2002-01-01" @default.
- W1972071232 modified "2023-10-15" @default.
- W1972071232 title "Time Change Representation of Stochastic Integrals" @default.
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- W1972071232 doi "https://doi.org/10.1137/s0040585x97979184" @default.
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