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Sub-value and sup-value of a linear diffusion game

Shangzhen Luo

Advances in Applied Probability2026https://doi.org/10.1017/apr.2025.10047article
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0.50

Abstract

In this paper, we solve an exit probability game between two players, each of whom controls a linear diffusion process. One player controls its process to minimize the probability that the difference of the processes reaches a low level before it reaches a high level, while the other player aims to maximize the probability. By solving the Bellman–Isaacs equations, we find the sub-value and sup-value functions of the game in explicit forms, which are twice continuously differentiable. The optimal plays associated with the sub-value and sup-value are also found explicitly.

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https://doi.org/https://doi.org/10.1017/apr.2025.10047

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@article{shangzhen2026,
  title        = {{Sub-value and sup-value of a linear diffusion game}},
  author       = {Shangzhen Luo},
  journal      = {Advances in Applied Probability},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1017/apr.2025.10047},
}

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0.50

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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