Partially Observed McKean--Vlasov Control with Vanishing Observation Intensities
Abstract
We study partially observed McKean--Vlasov jump-diffusions with controlled counting intensities that may vanish and depend on the unconditional physical state distribution. A deterministic upper bound on the likelihood supports one-sided state--likelihood variations, a smooth-test-function expansion of the physical state marginal, and a necessary maximum principle without inverse intensity or likelihood terms. We also establish a one-sided total-variation derivative of the physical probability on the fixed noise space, including a nonnegative singular component on baseline-null histories. A quadratic example shows, within a specified policy family and under explicit conditions, that positive variance feedback raises the first-order activation fee threshold while negative feedback lowers it.
Related
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BibTeX
@misc{xiong2026partially,
title = {{Partially Observed McKean--Vlasov Control with Vanishing Observation Intensities}},
author = {Jie Xiong and Ying Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29133},
eprint = {2610.29133},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29133},
}
RIS
TY - UNPB
TI - Partially Observed McKean--Vlasov Control with Vanishing Observation Intensities
AU - Jie Xiong
AU - Ying Yang
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29133
UR - https://arxiv.org/abs/2610.29133
AB - We study partially observed McKean--Vlasov jump-diffusions with controlled counting intensities that may vanish and depend on the unconditional physical state distribution. A deterministic upper bound on the likelihood supports one-sided state--likelihood variations, a smooth-test-function expansion of the physical state marginal, and a necessary maximum principle without inverse intensity or likelihood terms. We also establish a one-sided total-variation derivative of the physical probability on the fixed noise space, including a nonnegative singular component on baseline-null histories. A quadratic example shows, within a specified policy family and under explicit conditions, that positive variance feedback raises the first-order activation fee threshold while negative feedback lowers it.
ER -