Abstract:
We study the limit behavior of the canonical (i.e., degenerate) von Mises statistics based on samples from a sequence of weakly dependent stationary observations satisfying the $\psi$-mixing condition. The corresponding limit distributions are defined by the multiple stochastic integrals of nonrandom functions with respect to the nonorthogonal Hilbert noises generated by Gaussian processes with nonorthogonal increments.
Keywords:limit theorems, stochastic integral, multiple stochastic integral, elementary stochastic measure, Gaussian processes, stationary sequences of random variables, mixing, $U$- and $V$-statistics.
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