Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Independent increment processes: A multilinearity preserving property   We observe a multilinearity preserving property of conditional expectation
for infinite dimensional independent increment processes defined on some
abstract Banach space $B$. It is similar in nature to the polynomial preserving
property analysed greatly for finite dimensional stochastic processes and thus
offers an infinite dimensional generalisation. However, while polynomials are
defined using the multiplication operator and as such require a Banach algebra
structure, the multilinearity preserving property we prove here holds even for
processes defined on a Banach space which is not necessary a Banach algebra. In
the special case of $B$ being a commutative Banach algebra, we show that
independent increment processes are polynomial processes in a sense that
coincides with a canonical extension of polynomial processes from the finite
dimensional case. The assumption of commutativity is shown to be crucial and in
a non-commutative Banach algebra the multilinearity concept arises naturally.
Some of our results hold beyond independent increment processes and thus shed
light on infinite dimensional polynomial processes in general.

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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat