Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinite dimensional Ornstein-Uhlenbeck processes with unbounded
  diffusion - Approximation, quadratic variation, and It\^o formula   The paper studies a class of Ornstein-Uhlenbeck processes on the classical
Wiener space. These processes are associated with a diffusion type Dirichlet
form whose corresponding diffusion operator is unbounded in the Cameron-Martin
space. It is shown that the distributions of certain finite dimensional
Ornstein-Uhlenbeck processes converge weakly to the distribution of such an
infinite dimensional Ornstein-Uhlenbeck process. For the infinite dimensional
processes, the ordinary scalar quadratic variation is calculated. Moreover,
relative to the stochastic calculus via regularization, the scalar as well as
the tensor quadratic variation are derived. A related It\^o formula is
presented.

21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph