Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multivariate COGARCH(1,1) processes   Multivariate $\operatorname {COGARCH}(1,1)$ processes are introduced as a
continuous-time models for multidimensional heteroskedastic observations. Our
model is driven by a single multivariate L\'{e}vy process and the latent
time-varying covariance matrix is directly specified as a stochastic process in
the positive semidefinite matrices. After defining the $\operatorname
{COGARCH}(1,1)$ process, we analyze its probabilistic properties. We show a
sufficient condition for the existence of a stationary distribution for the
stochastic covariance matrix process and present criteria ensuring the
finiteness of moments. Under certain natural assumptions on the moments of the
driving L\'{e}vy process, explicit expressions for the first and second-order
moments and (asymptotic) second-order stationarity of the covariance matrix
process are obtained. Furthermore, we study the stationarity and second-order
structure of the increments of the multivariate $\operatorname {COGARCH}(1,1)$
process and their "squares".

23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn