Stochastic Control Theory: Dynamic Programming Principle
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Discontinuous phase transitions in information-processing strategies have also been reported within the information bottleneck framework.
“Discontinuous phase transitions in informationprocessing strategies have also been reported within the information bottleneck framework [38-42].”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [40]
Eq. (S6) is similar to the Riccati equation in standard optimal control theory, but has an additional last term because the work considers partial and noisy observations.
“Eq. (S6) is similar to the Riccati equation in the standard optimal control theory [10-12], but the last term is additional because this work considers partial and noisy observations.”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [11]
Cites
Dubins, L. E., & Schwarz, G. E. (1965) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.53.5.913 · Cited by 181 · see citing works
Uniqueness of Viscosity Solutions
Lindqvist, P. (2016) · SpringerBriefs in mathematics · doi:10.1007/978-3-319-31532-4_8 · Cited by 2 · see citing works
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Memory-Limited Partially Observable Stochastic Control and Its Mean-Field Control Approach
Tottori, T., & Kobayashi, T. J. (2022) · Entropy · doi:10.3390/e24111599 · Cited by 11 · see citing works
Tottori, T., & Kobayashi, T. J. (2023) · Entropy · doi:10.3390/e25020208 · Cited by 11 · see citing works
Decentralized Stochastic Control with Finite-Dimensional Memories: A Memory Limitation Approach
Tottori, T., & Kobayashi, T. J. (2023) · Entropy · doi:10.3390/e25050791 · Cited by 7 · see citing works
Tottori, T., & Kobayashi, T. J. (2025) · Physical Review Research · doi:10.1103/gvl6-cvby · Cited by 6 · see citing works
Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies
Tottori, T., & Kobayashi, T. J. (2026) · Physical Review Letters · doi:10.1103/5ynb-7k4v
- Authors
- Nisio, M.
- Affiliations
- Kobe University (JP)
- Corresponding author
- Nisio, Makiko
- Venue
- Probability Theory and Stochastic Modelling
- Publisher
- Springer Japan
- Published
- 2015
- ISSN
- 2199-3130 (ISSN-L)
- 2199-3149
- OpenAlex
- W2498807917
- Cited by
- 67
- References
- 2
- Citations by year
- 2026: 7 · 2025: 9 · 2024: 4 · 2023: 5 · 2022: 3 · 2021: 7 · 2020: 5 · 2019: 7 · 2018: 9 · 2017: 2 · 2016: 1 · 2015: 1 · 2014: 2
- FWCI
- 2.11
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- Locations
- Probability theory and stochastic modelling (publishedVersion)
- International Linear Collider (submittedVersion)
- Digital Access to Libraries (Université catholique de Louvain (UCL), l'Université de Namur (UNamur) and the Université Saint-Louis (USL-B)) (submittedVersion)
- Topics
- Social Sciences › Economics, Econometrics and Finance › Finance › Stochastic processes and financial applications
- Physical Sciences › Mathematics › Applied Mathematics › Nonlinear Partial Differential Equations
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Adaptive Dynamic Programming Control
- Keywords
- stochastic optimal control, dynamic programming principle, nonlinear semigroups, Hamilton-Jacobi-Bellman equation, viscosity solutions, American option pricing, stochastic differential games, Isaacs equation, Zakai equation, parabolic stochastic partial differential equations, value function
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