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Mean-field stochastic differential equations driven by sub-diffusions and their control problem

  • Shuaiqi Zhang
  • Zhen-Qing Chen
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Abstract

In this paper, we establish the existence and uniqueness of solutions for mean-field stochastic differential equations (MF-SDEs in short) and backward stochastic differential equations (MF-BSDE) driven by anomalous sub-diffusions {BLt; t≥ 0} with random coefficients, respectively. Here B is a Brownian motion on ℝd and L is the inverse of a subordinator S with drift κ>0 that is independent of B. We further study the stochastic maximum principles (SMPs) for control problems of the stochastic systems modelled by the MF-SDEs using a convex variational method. A linear quadratic control example is given in the last section of this paper, for which both the SMP and the sufficient SMP established in this paper are utilized to show explicitly that it admits a unique stochastic optimal control.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026meanfield,
  title = {{Mean-field stochastic differential equations driven by sub-diffusions and their control problem}},
  author = {Shuaiqi Zhang and Zhen-Qing Chen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22883},
  eprint = {2609.22883},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22883},
}
RIS
TY  - UNPB
TI  - Mean-field stochastic differential equations driven by sub-diffusions and their control problem
AU  - Shuaiqi Zhang
AU  - Zhen-Qing Chen
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.22883
UR  - https://arxiv.org/abs/2609.22883
AB  - In this paper, we establish the existence and uniqueness of solutions for mean-field stochastic differential equations (MF-SDEs in short) and backward stochastic differential equations (MF-BSDE) driven by anomalous sub-diffusions {B_L_t; t≥ 0} with random coefficients, respectively. Here B is a Brownian motion on ℝ^d and L is the inverse of a subordinator S with drift κ>0 that is independent of B. We further study the stochastic maximum principles (SMPs) for control problems of the stochastic systems modelled by the MF-SDEs using a convex variational method. A linear quadratic control example is given in the last section of this paper, for which both the SMP and the sufficient SMP established in this paper are utilized to show explicitly that it admits a unique stochastic optimal control.
ER  -