Summary
If (Y i) and (V i) are independent random sequences such thatY i are i.i.d. random variables belonging to the normal domain of attraction of a symmetric α-stable law, 0<α<2, andV i are i.i.d. random variables, then the limit distributions of U-statistics\(n^{ - 1/\alpha } \sum\limits_{1 \leqq i_t , \ldots ,i_d \leqq n} {Y_{i_1 } \ldots Y_{i_d } f(V_{i_1 } , \ldots ,V_{i_d } )} \), coincide with the probability laws of multiple stochastic integralsX d f =∫ ...∫ f (t 1, ... ,t d)dX(t d) with respect to a symmetric α-stable processX(t).
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The research was originated during author's visit at ORIE, Cornell University
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Szulga, J. Limit distributions of U-statistics resampled by symmetric stable laws. Probab. Th. Rel. Fields 94, 83–90 (1992). https://doi.org/10.1007/BF01222511
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DOI: https://doi.org/10.1007/BF01222511