Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tail estimates for stochastic fixed point equations via nonlinear
  renewal theory   This paper presents precise large deviation estimates for solutions to
stochastic fixed point equations of the type V =_d f(V), where f(v) = Av + g(v)
for a random function g(v) = o(v) a.s. as v tends to infinity. Specifically, we
provide an explicit characterization of the pair (C,r) in the tail estimate P(V
> u) ~ C u^-r as u tends to infinity, and also present a Lundberg-type upper
bound of the form P(V > u) <= D(u) u^-r. To this end, we introduce a novel dual
change of measure on a random time interval and analyze the path properties,
using nonlinear renewal theory, of the Markov chain resulting from the forward
iteration of the given stochastic fixed point equation. In the process, we
establish several new results in the realm of nonlinear renewal theory for
these processes. As a consequence of our techniques, we also establish a new
characterization of the extremal index. Finally, we provide some extensions of
our methods to Markov-driven sequences.

37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc