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XIAO Li-shun, LI Hui-ying, FAN Sheng-jun. One-dimensional BSDEs with monotonic, H\'{o}lder continuous and Integrable parameters[J]. Journal of East China Normal University (Natural Sciences), 2012, (1): 130-137.
Citation:
XIAO Li-shun, LI Hui-ying, FAN Sheng-jun. One-dimensional BSDEs with monotonic, H\"{o}lder continuous and Integrable parameters[J]. Journal of East China Normal University (Natural Sciences), 2012, (1): 130-137.
XIAO Li-shun, LI Hui-ying, FAN Sheng-jun. One-dimensional BSDEs with monotonic, H\'{o}lder continuous and Integrable parameters[J]. Journal of East China Normal University (Natural Sciences), 2012, (1): 130-137.
Citation:
XIAO Li-shun, LI Hui-ying, FAN Sheng-jun. One-dimensional BSDEs with monotonic, H\"{o}lder continuous and Integrable parameters[J]. Journal of East China Normal University (Natural Sciences), 2012, (1): 130-137.
This paper established a new existence and uniqueness result for solutions to one-dimensional backward stochastic differential equations (BSDEs) with only integrable parameters, where the generator $g$ is monotonic in $y$ and $\alpha$-H\{o}lder ($0\alpha1$) continuous in $z$. By Tanaka's formula and Girsanov's theorem we established a comparison theorem for solutions in $L^1$ to BSDEs, from which the uniqueness follows. By convolution technique we obtained a uniform approximation sequence of the generator $g$ and then constructed a sequence of solutions in $L^1$ for BSDEs. Finally, we proved the limitation of this sequence of solutions is the desired solution. This proved the existence.
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