Abstract
In this chapter, we develop some filtering results for the solutions to BSDEs and FBSDEs, which play an important role in studying the optimal control with incomplete information. We first state a theorem on the stochastic filtering of a general stochastic process. The proof of that result can be found in Liptser and Shiyayev [49], so we omit it here. Then, we apply this result to the stochastic filtering for the solutions to BSDEs in Section 3.2 and to those for FBSDEs in Section 3.3.
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Wang, G., Wu, Z., Xiong, J. (2018). Filtering of BSDE and FBSDE. In: An Introduction to Optimal Control of FBSDE with Incomplete Information. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-79039-8_2
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DOI: https://doi.org/10.1007/978-3-319-79039-8_2
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