Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transformations of L\'evy Processes   A L\'evy process on a *-bialgebra is given by its generator, a conditionally
positive hermitian linear functional vanishing at the unit element. A *-algebra
homomorphism k from a *-bialgebra C to a *-bialgebra B with the property that k
respects the counits maps generators on B to generators on C. A tranformation
between the corrresponding two L\'evy processes is given by forming
infinitesimal convolution products.
  This general result is applied to various situations, e.g., to a *-bialgebra
and its associated primitive tensor *-bialgebra (called "generator process") as
well as its associated group-like *-bialgebra (called Weyl-*-bialgebra). It
follows that a L\'evy process on a *-bialgebra can be realized on Bose Fock
space as the infinitesimal convolution product of its generator process such
that the vacuum vector is cyclic for the L\e'vy process. Moreover, we obtain
convolution approximations of the Az\'ema martingale by the Wiener process and
vice versa.

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The categories of this paper are: nlin
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The categories of this paper are: stat
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph