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| Probabilistic Interpretation for a System of Quasilinear ParabolicPartial Differential-Algebraic Equations: The Classical Solution |
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Citation： |
Zhen WU · Bing XIE · Zhiyong YU.Probabilistic Interpretation for a System of Quasilinear ParabolicPartial Differential-Algebraic Equations: The Classical Solution[J].Chinese Annals of Mathematics B,2025,46(6):875~950 |
| Page view： 104
Net amount： 48 |
Authors： |
Zhen WU · Bing XIE · Zhiyong YU; |
Foundation： |
This work was supported by the National Key Research and Development Program of China
(No. 2023YFA1009200), the National Natural Science Foundation of China (Nos. 12521001, 12271304,
62561160159), the Natural Science Foundation of Shandong Province (No. ZR2024ZD35) and the Taishan Scholars Climbing Program of Shandong Province (No. TSPD20210302). |
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| Abstract： |
In the present paper, by introducing a family of coupled forward-backward
stochastic differential equations (FBSDEs for short), a probabilistic interpretation for a
system consisting of m second order quasilinear (and possibly degenerate) parabolic partial
differential equations and (m × d) algebraic equations is given in the sense of the classical
solution. For solving the problem, an Lp-estimate (p > 2) for coupled FBSDEs on large
time durations in the monotonicity framework is established, and a new method to analyze
the regularity of solutions to FBSDEs is introduced. The new method avoids the use
of Kolmogorov’s continuity theorem and only employs L2-estimates and L4-estimates to
obtain the desired regularity. |
Keywords： |
Forward-backward stochastic differential equation, Monotonicity condition, Parabolic partial differential equation, Classical solution |
Classification： |
60H10, 35K59, 35C99 |
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