Bellman functions and continuous time
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Komla Domelevo
Abstract
The purpose of this text is both instructive and historic. We give a review of the classical Bellman technique mainly in the “weak” (dualized) form for dyadic martingales. From here, we approach techniques and novelties required to pass to their use for continuous time martingales with jumps. The historic part shows the development in dyadic analysis of a Bellman function for a specific problem. We then study this Bellman function and show it has some additional properties, useful for the analogous question in the continuous case.
Abstract
The purpose of this text is both instructive and historic. We give a review of the classical Bellman technique mainly in the “weak” (dualized) form for dyadic martingales. From here, we approach techniques and novelties required to pass to their use for continuous time martingales with jumps. The historic part shows the development in dyadic analysis of a Bellman function for a specific problem. We then study this Bellman function and show it has some additional properties, useful for the analogous question in the continuous case.
Kapitel in diesem Buch
- Frontmatter I
- Contents V
- Algebraically integrable bodies and related properties of the Radon transform 1
- The covariogram problem 37
- The logarithmic Minkowski conjecture and the Lp-Minkowski problem 83
- Bellman functions and continuous time 119
- Volume product 163
- Inequalities for sections and projections of convex bodies 223
- Borderline estimates for weighted singular operators and concavity 257
- Extremal sections and projections of certain convex bodies: a survey 343
- When does e−/τ/ maximize Fourier extension for a conic section? 391
- Affine surface area 427
- Analysis and geometry near the unit ball: proofs, counterexamples, and open questions 445
- Index 469
Kapitel in diesem Buch
- Frontmatter I
- Contents V
- Algebraically integrable bodies and related properties of the Radon transform 1
- The covariogram problem 37
- The logarithmic Minkowski conjecture and the Lp-Minkowski problem 83
- Bellman functions and continuous time 119
- Volume product 163
- Inequalities for sections and projections of convex bodies 223
- Borderline estimates for weighted singular operators and concavity 257
- Extremal sections and projections of certain convex bodies: a survey 343
- When does e−/τ/ maximize Fourier extension for a conic section? 391
- Affine surface area 427
- Analysis and geometry near the unit ball: proofs, counterexamples, and open questions 445
- Index 469
