Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Backward stochastic dynamics on a filtered probability space   We demonstrate that backward stochastic differential equations (BSDE) may be
reformulated as ordinary functional differential equations on certain path
spaces. In this framework, neither It\^{o}'s integrals nor martingale
representation formulate are needed. This approach provides new tools for the
study of BSDE, and is particularly useful for the study of BSDE with partial
information. The approach allows us to study the following type of backward
stochastic differential equations: \[dY_t^j=-f_0^j(t,Y_t,L(M)_t)
dt-\sum_{i=1}^df_i^j(t,Y_t), dB_t^i+dM_t^j\] with $Y_T=\xi$, on a general
filtered probability space $(\Omega,\mathcal{F},\mathcal{F}_t,P)$, where $B$ is
a $d$-dimensional Brownian motion, $L$ is a prescribed (nonlinear) mapping
which sends a square-integrable $M$ to an adapted process $L(M)$ and $M$, a
correction term, is a square-integrable martingale to be determined. Under
certain technical conditions, we prove that the system admits a unique solution
$(Y,M)$. In general, the associated partial differential equations are not only
nonlinear, but also may be nonlocal and involve integral operators.

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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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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: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: physics