70 research outputs found
Large versus bounded solutions to sublinear elliptic problems
Let be a second order elliptic operator with smooth coefficients defined
on a domain (possibly unbounded), . We
study nonnegative continuous solutions to the equation on ,
where is in the Kato class with respect to the first variable and
it grows sublinearly with respect to the second variable. Under fairly general
assumptions we prove that if there is a bounded non zero solution then there is
no large solution
Diagonal stochastic recurrence equation -- multivariate regular variation
Multivariate process satisfying affine stochastic recurrence equation with
generic diagonal matrices is considered. We prove that the stationary solution
is regularly varying. The results are applicable to diagonal autoregressive
models.Comment: 21 page
Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems
Let be an i.i.d. sequence of Lipschitz mappings of . We study
the Markov chain on defined by the recursion
, , . We assume that
for a fixed continuous function , commuting with dilations and i.i.d random pairs ,
where and is a continuous mapping of .
Moreover, is -regularly varying and has a faster decay at
infinity than . We prove that the stationary measure of the Markov
chain is -regularly varying. Using this result we show
that, if , the partial sums , appropriately
normalized, converge to an -stable random variable. In particular, we
obtain new results concerning the random coefficient autoregressive process
.Comment: 23 pages, 0 figures. Accepted for publication in Stochastic Processes
and their Application
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