Infinitesimal methods in control theory: deterministic and stochastic
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Publication:1071249
DOI10.1007/BF00046584zbMath0585.49005OpenAlexW2035331885MaRDI QIDQ1071249
Publication date: 1986
Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf00046584
nonstandard analysisrelaxed controlsdeterministic controlpartially observed stochastic controlLoeb spacesdigital read-out
Optimal stochastic control (93E20) Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for optimal control problems involving ordinary differential equations (49J15) Nonstandard models in mathematics (03H05) Existence of optimal solutions to problems involving randomness (49J55) Nonstandard analysis (26E35)
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Cites Work
- Unnamed Item
- On the existence of optimal partially observed controls
- A non-standard representation for Brownian motion and Ito integration
- Nonstandard Measure Theory and its Applications
- An infinitesimal approach to stochastic analysis
- On the existence of solutions to stochastic differential equations on Loeb spaces
- Star-Finite Representations of Measure Spaces
- SOME ESTIMATES OF THE PROBABILITY DENSITY OF A STOCHASTIC INTEGRAL
- Conversion from Nonstandard to Standard Measure Spaces and Applications in Probability Theory
- Weak Limits of Measures and the Standard Part Map
- Optimal controls for partially observed stochastic systems: an infinitesimal approach