Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unifying the Dynkin and Lebesgue-Stieltjes formulae   We establish a local martingale $M$ associate with $f(X,Y)$ under some
restrictions on $f$, where $Y$ is a process of bounded variation (on compact
intervals) and either $X$ is a jump diffusion (a special case being a L\'evy
process) or $X$ is some general (c\'adl\'ag metric space valued) Markov
process. In the latter case $f$ is restricted to the form
$f(x,y)=\sum_{k=1}^K\xi_k(x)\eta_k(y)$. This local martingale unifies both
Dynkin's formula for Markov processes and the Lebesgue-Stieltjes integration
(change of variable) formula for (right continuous) functions of bounded
variation. For the jump diffusion case, when further relatively easily
verifiable conditions are assumed then this local martingale becomes an $L^2$
martingale. Convergence of the product of this Martingale with some
deterministic function (of time) to zero both in $L^2$ and a.s. is also
considered and sufficient conditions for functions for which this happens are
identified.

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The categories of this paper are: cs
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an