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Statistics Seminar, "Normal approximation for time-dependent dynamical systems by Stein’s method", Juho Leppänen, University of Paris

Seminarium

Tid: 2019-03-01 13:15 till: 14:00
Plats: MH:227
Kontakt: dragi [at] maths [dot] lth [dot] se
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In 1972, Charles Stein introduced an unusual method for estimating
the distance between a probability distribution and a normal distribution. The
method is based on an inhomogeneous differential equation which turns the
problem of normal approximation into a problem of bounding the expectation of a
certain functional of the random variable in question. Stein’s method has
proved very useful for estimating the error in the CLT under various dependence
structures.

I will describe an adaptation of Stein’s method for dynamical systems, which
yields certain correlation-decay conditions for a multivariate central limit
theorem augmented by a rate of convergence. The adaptation is especially suited
for normal approximation of time-dependent systems in which the evolution of
states is described by a family of varying maps, rather than a single map. I
will mention some applications for expanding and intermittent systems.