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http://hdl.handle.net/10603/428875
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DC Field | Value | Language |
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dc.coverage.spatial | ||
dc.date.accessioned | 2022-12-20T10:40:51Z | - |
dc.date.available | 2022-12-20T10:40:51Z | - |
dc.identifier.uri | http://hdl.handle.net/10603/428875 | - |
dc.description.abstract | This thesis studies risk-sensitive stochastic optimal control and differential game problems. First, we study risk-sensitive stochastic differential games for controlled reflecting diffusion processes in a smooth bounded domain in Rd . We consider both nonzero-sum and zero-sum cases. We treat two cost evaluation criteria namely discounted cost and ergodic cost. Under certain assumptions, we establish the existence of a Nash/saddle-point equilibria for relevant cases. For ergodic cost criterion, we use principal eigenvalue approach to study the game problems. This approach enables us to obtain a complete characterization of Nash/saddle point equilibrium in the space of stationaryMarkov strategies. Subsequently, we study risk-sensitive ergodic control problem for controlled reflecting diffusion processes in the non-negative orthant. Under a certain Lyapunov type stability assumption and some other technical assumptions, we first establish the existence of a solution to the multiplicative Poisson equation for each stationary Markov control. Using this result, we establish the existence of a unique solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation. This, in turn, leads to the complete characterization of optimal control in the space of stationary Markov controls. Then we study risk-sensitive zero-sum/nonzero-sumstochastic differential games on the infinite horizon, where the state is a controlled reflecting diffusion in the nonnegative orthant. We consider two cost evaluation criteria: discounted cost and ergodic cost. Under certain assumptions,we establish the existence of a saddle point/Nash equilibria, for relevant cases. We obtain our results by studying the corresponding Hamilton-Jacobi-Isaacs (HJI)/coupled HJB equations. For the ergodic cost criterion, we completely characterize a saddle point/Nash equilibria in the space of stationary strategies... | |
dc.format.extent | xi, 181 p. | |
dc.language | English | |
dc.relation | ||
dc.rights | university | |
dc.title | Risk Sensitive Stochastic Control and Differential Games | |
dc.title.alternative | Risk-Sensitive Stochastic Control and Differential Games | |
dc.creator.researcher | Pradhan, Somnath | |
dc.subject.keyword | Mathematics | |
dc.subject.keyword | Physical Sciences | |
dc.description.note | ||
dc.contributor.guide | Ghosh, Mrinal K | |
dc.publisher.place | Bangalore | |
dc.publisher.university | Indian Institute of Science Bangalore | |
dc.publisher.institution | Mathematics | |
dc.date.registered | ||
dc.date.completed | 2019 | |
dc.date.awarded | 2019 | |
dc.format.dimensions | 30 cm. | |
dc.format.accompanyingmaterial | None | |
dc.source.university | University | |
dc.type.degree | Ph.D. | |
Appears in Departments: | Mathematics |
Files in This Item:
File | Description | Size | Format | |
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01_title.pdf | Attached File | 80.4 kB | Adobe PDF | View/Open |
02_prelim pages.pdf | 75.13 kB | Adobe PDF | View/Open | |
03_table of content.pdf | 54.25 kB | Adobe PDF | View/Open | |
04_abstract.pdf | 74.39 kB | Adobe PDF | View/Open | |
05_chapter 1.pdf | 146.34 kB | Adobe PDF | View/Open | |
06_chapter 2.pdf | 203.38 kB | Adobe PDF | View/Open | |
07_chapter 3.pdf | 213.48 kB | Adobe PDF | View/Open | |
08_chapter 4.pdf | 222.4 kB | Adobe PDF | View/Open | |
09_chapter 5.pdf | 278.23 kB | Adobe PDF | View/Open | |
10_chapter 6.pdf | 224.41 kB | Adobe PDF | View/Open | |
11_chapter 7.pdf | 208.57 kB | Adobe PDF | View/Open | |
12_annexure.pdf | 97 kB | Adobe PDF | View/Open | |
80_recommendation.pdf | 152.78 kB | Adobe PDF | View/Open |
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