More on P-stable convex sets in Banach spaces

We study the asymptotic behavior and limit distributions for sums S-n= b(n) (-1) Sigma(i)(n) (=1) xi(i), where xi(i), i greater than or equal to 1, are i.i.d. random convex compact ice sets in a given separable Banach space B and summation is defined in a sense of Minkowski. The following results are obtained: iii Series (LePage type) and Poisson integral representations of random stable cc sets in B are established; (iii) The invariance principle For processes S-n(t) = b(n)(-1) Sigma(i = 1)([nt]) xi(i), t epsilon [0, 1] , and the existence of p-stable cc Levy motion are proved: (iii) In the cas e, uht rr fi are segments, the limit of S-n is proved to be countable zonot ope. Furthermore, if B = R-d, the singularity of distributions of two count able zonotopes Yp(1), sigma(1), Y-p2, (sigma 2), corresponding to values of exponents p(1) not equal p(2) and spectral measures sigma(1),. a,, is prov ed if either p(1) not equal p(2) or sigma(1) not equal sigma(2); (iv) Some new simple estimates of parameters of stable laws in R-d, bastld on these r esults are suggested.