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A noncommunicative Kalman condition for null controllability of backward stochastic parabolic systems
Abstract
We study null controllability of backward stochastic heat systems with constant couplings in both the state and the martingale integrand, common scalar diffusion, and a localized drift control. We prove that null controllability is equivalent to a noncommutative word-rank condition on the two coupling matrices and the control matrix. The proof combines a factorization of the dual dynamics, positivity and small-time coercivity of a finite-dimensional stochastic Gramian, and a Lebeau--Robbiano spectral argument. Failure of the rank condition yields an invariant unobservable subspace.
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BibTeX
@misc{fadili2026noncommunicative,
title = {{A noncommunicative Kalman condition for null controllability of backward stochastic parabolic systems}},
author = {Mohamed Fadili},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.01836},
eprint = {2608.01836},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.01836},
}
RIS
TY - UNPB
TI - A noncommunicative Kalman condition for null controllability of backward stochastic parabolic systems
AU - Mohamed Fadili
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2608.01836
UR - https://arxiv.org/abs/2608.01836
AB - We study null controllability of backward stochastic heat systems with constant couplings in both the state and the martingale integrand, common scalar diffusion, and a localized drift control. We prove that null controllability is equivalent to a noncommutative word-rank condition on the two coupling matrices and the control matrix. The proof combines a factorization of the dual dynamics, positivity and small-time coercivity of a finite-dimensional stochastic Gramian, and a Lebeau--Robbiano spectral argument. Failure of the rank condition yields an invariant unobservable subspace.
ER -