Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cylindrical continuous martingales and stochastic integration in
  infinite dimensions   In this paper we define a new type of quadratic variation for cylindrical
continuous local martingales on an infinite dimensional spaces. It is shown
that a large class of cylindrical continuous local martingales has such a
quadratic variation. For this new class of cylindrical continuous local
martingales we develop a stochastic integration theory for operator valued
processes under the condition that the range space is a UMD Banach space. We
obtain two-sided estimates for the stochastic integral in terms of the
$\gamma$-norm. In the scalar or Hilbert case this reduces to the
Burkholder-Davis-Gundy inequalities. An application to a class of stochastic
evolution equations is given at the end of the paper.

25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg