Functional limit theorems for random quadratic forms

We prove a functional central limit theorem and a functional law of the iterated logarithm for quadratic forms in independent random variables.

[1]  V. Rotaŕ,et al.  On the Rate of Convergence in the Limit Theorem for Quadratic Forms , 1978 .

[2]  V. Rotaŕ.  Some Limit Theorems for Polynomials of Second Degree , 1974 .

[3]  A Nonuniform Bound on the Rate of Convergence in the Martingale Central Limit Theorem , 1988 .

[4]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[5]  J. Szulga,et al.  Random Multilinear Forms , 1986 .

[6]  B. M. Brown,et al.  Martingale Central Limit Theorems , 1971 .

[7]  P. Guttorp,et al.  On the asymptotic distribution of quadratic forms in uniform order statistics , 1988 .

[8]  F. T. Wright,et al.  The Almost Sure Stability of Quadratic Forms , 1979 .

[9]  Stability of quadratic forms in independent random variables in Banach spaces , 1981 .

[10]  Stamatis Cambanis,et al.  Convergence of Quadratic Forms in p-Stable Random Variables and Theta sub p-Radonifying Operators. , 1985 .

[11]  V. V. Petrov.  Sums of Independent Random Variables , 1975 .

[12]  W. Stout.  Almost sure convergence , 1974 .

[13]  T. Mikosch.  Bounded laws of the iterated logarithm for quadratic forms in Gaussian random variables , 1988 .

[14]  Wojbor A. Woyczyński,et al.  Double Stochastic Integrals, Random Quadratic Forms and Random Series in Orlicz Spaces , 1987 .

[15]  V. Strassen.  An invariance principle for the law of the iterated logarithm , 1964 .

[16]  V. Rotaŕ.  Limit Theorems for Multilinear Forms and Quasipolynomial Functions , 1976 .

[17]  F. T. Wright,et al.  Convergence results for sequences of quadratic forms , 1982 .

[18]  Peter F. de Jong,et al.  A central limit theorem for generalized quadratic forms , 1987 .

[19]  T. Mikosch.  The rate of convergence in the functional central limit theorem for random quadratic forms with some applications to the law of the iterated logarithm , 1989 .

[20]  D. Varberg.  Convergence of Quadratic Forms in Independent Random Variables , 1966 .

[21]  On the convergence of bilinear and quadratic forms in independent random variables , 1982 .

[22]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[23]  H. Teicher,et al.  Stability of Random Variables and Iterated Logarithm Laws for Martingales and Quadratic Forms , 1980 .

[24]  P. Billingsley,et al.  Convergence of Probability Measures , 1969 .