JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (10): 46-52.doi: 10.6040/j.issn.1671-9352.0.2023.281

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Sufficient maximum principle for one kind of nonzero-sum stochastic differential game involving noisy memory

Feng ZHANG(),Jiawei LIANG   

  1. School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, Shandong, China
  • Received:2023-06-27 Online:2024-10-20 Published:2024-10-10

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Abstract:

One nonzero-sum stochastic differential game is considered, whose main feature is that several kinds of delays of the state and the control are involved. The state process can contain distributed delays, discrete delays, and noisy memory, and control processes can contain distributed delays and discrete delays. The control domains are convex sets. Sufficient conditions for the equilibrium point of the game are established by means of the stochastic maximum principle. Finally, an illustrative example is considered for which the equilibrium point is obtained in explicit form.

Key words: nonzero-sum stochastic differential game, delay, noisy memory, equilibrium point, maximum principle

CLC Number: 

  • O232
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