94,013 research outputs found
Sums and averages
These informal notes are concerned with sums and averages in various
situations in analysis.Comment: 51 page
Periodic orbit sum rules for billiards: Accelerating cycle expansions
We show that the periodic orbit sums for 2-dimensional billiards satisfy an
infinity of exact sum rules. We test such sum rules and demonstrate that they
can be used to accelerate the convergence of cycle expansions for averages such
as Lyapunov exponents.Comment: 19 pages, 5 postscript figures, submitted to Journal of Physics
Weak convergence of sums of moving averages in the α-stable domain of attraction
Skorohod has shown that the convergence of sums of i.i.d. random variables to an a-stable Levy motion, with 0 < a < 2, holds in the weak-J1 sense. J1 is the commonly used Skorohod topology. We show that for sums of moving averages with at least two nonzero coefficients, weak-J1 conver- gence cannot hold because adjacent jumps of the process can coalesce in the limit; however, if the moving average coefficients are positive, then the adjacent jumps are essentially monotone and one can have weak-M1 con- vergence. M1 is weaker than J1, but it is strong enough for the sup and inf functionals to be continuous
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