Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Incremental Nonlinear Stability Analysis of Stochastic Systems Perturbed
  by L\'{e}vy Noise   We present a theoretical framework for characterizing incremental stability
of nonlinear stochastic systems perturbed by compound Poisson shot noise and
finite-measure L\'{e}vy noise. For each noise type, we compare trajectories of
the perturbed system with distinct noise sample paths against trajectories of
the nominal, unperturbed system. We show that for a finite number of jumps
arising from the noise process, the mean-squared error between the trajectories
exponentially converge towards a bounded error ball across a finite interval of
time under practical boundedness assumptions. The convergence rate for shot
noise systems is the same as the exponentially-stable nominal system, but with
a tradeoff between the parameters of the shot noise process and the size of the
error ball. The convergence rate and the error ball for the L\'{e}vy noise
system are shown to be nearly direct sums of the respective quantities for the
shot and white noise systems separately, a result which is analogous to the
L\'{e}vy-Khintchine theorem. We demonstrate our results using several simple
case studies: a 1D linear reference-tracking system, 2D linear time-varying
systems, a 2D nonlinear system, and a 2D nonlinear observer design problem.

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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph