Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential ergodicity for diffusions with jumps driven by a Hawkes
  process   In this paper, we introduce a new class of processes which are diffusions
with jumps driven by a multivariate nonlinear Hawkes process. Our goal is to
study their long-time behavior. In the case of exponential memory kernels for
the underlying Hawkes process we establish conditions for the positive Harris
recurrence of the couple (X, Y), where X denotes the diffusion process and Y
the piecewise deterministic Markov process (PDMP) defining the stochastic
intensity of the driving Hawkes. As a direct consequence of the Harris
recurrence, we obtain the ergodic theorem for X. Furthermore, we provide
sufficient conditions under which the process is exponentially $\beta$--mixing.

3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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The categories of this paper are: nlin
17
The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas