h1

% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@PHDTHESIS{SubbiahPillai:1013009,
      author       = {Subbiah Pillai, Shyam Mohan},
      othercontributors = {Tempone, Raul and Ben Rached, Nadhir and Jasra, Ajay},
      title        = {{N}umerical methods for stochastic optimal control:
                      applications in rare event estimation and wireless networks},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      publisher    = {RWTH Aachen University},
      reportid     = {RWTH-2025-05282},
      pages        = {1 Online-Ressource : Illustrationen},
      year         = {2025},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, RWTH Aachen University, 2025},
      abstract     = {This thesis develops numerical methods for non-standard
                      stochastic optimal control (SOC) problems, driven by
                      real-world applications in rare event estimation and
                      energy-efficient wireless networks. The underlying process
                      models are controlled stochastic differential equations. In
                      the first part, we introduce an efficient Monte Carlo (MC)
                      estimator of rare event probabilities associated with the
                      McKean--Vlasov stochastic differential equation, crucial for
                      analysing mean-field systems in statistical physics,
                      mathematical finance and many more applications. Using SOC,
                      we derive an optimal importance sampling (IS) measure change
                      that minimises the estimator's relative statistical error.
                      We then combine IS with hierarchical sampling techniques,
                      like multilevel and multi-index MC, to enhance its
                      computational complexity. The resulting multi-index double
                      loop MC estimator achieves a significantly improved
                      computational complexity of $O(TOL^{-2}$
                      $log(TOL^{-1})^{2})$ for estimating rare event probabilities
                      with a prescribed relative accuracy TOL. In the second part,
                      we develop a modelling and numerical framework to solve a
                      chance-constrained SOC problem in cellular wireless
                      networks, where the objective is to compute an optimal
                      short-term power procurement strategy that minimises both
                      operating expenditure and carbon footprint. The model
                      accounts for uncertain renewable energy sources, stochastic
                      wireless channels, and a probabilistic quality-of-service
                      (QoS) constraint, making it a challenging SOC problem. The
                      solution procedure involves a continuous-time Lagrangian
                      relaxation of the QoS constraint, a computationally
                      efficient numerical scheme to solve the
                      Hamilton--Jacobi--Bellman partial differential equation
                      associated with the relaxed problem, and an optimisation
                      framework for the non-smooth dual problem, enabling
                      effective handling of the probabilistic constraint. The
                      proposed numerical procedure provides near-optimal policies
                      for a model cellular base station powered by a hybrid energy
                      system, using German grid and cellular user data. Results
                      demonstrate that our approach delivers solutions in a
                      practical time-frame, emphasising its computational
                      efficiency and real-world applicability.},
      cin          = {118110 / 110000},
      ddc          = {510},
      cid          = {$I:(DE-82)118110_20190107$ / $I:(DE-82)110000_20140620$},
      pnm          = {HDS LEE - Helmholtz School for Data Science in Life, Earth
                      and Energy (HDS LEE) (HDS-LEE-20190612) /
                      Doktorandenprogramm (PHD-PROGRAM-20170404)},
      pid          = {G:(DE-Juel1)HDS-LEE-20190612 /
                      G:(DE-HGF)PHD-PROGRAM-20170404},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2025-05282},
      url          = {https://publications.rwth-aachen.de/record/1013009},
}