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| HAL: hal-00662973, version 1 |
| arXiv: 1201.5454 |
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| BMO Martingales and Positive Solutions of Heat Equations |
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| Ying Hu 1Zhongmin Qian 2 |
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| (2012-01-25) |
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| In this paper, we establish two new estimates concerning positive solutions of a linear parabolic equation. More precisely, we give explicit estimates of the gradient of logarithm of a positive solution via the uniform bound of the logarithm of the solution. Moreover, we give a generalized version of Li-Yau's estimate. Our proof is based on the link between PDE and quadratic BSDE. |
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| 1: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 2: | Mathematical Institute [Oxford] (MI) |
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University of Oxford |
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| Processus stochastiques |
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| Subject | : | Mathematics/Probability |
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| hal-00662973, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00662973 | |
| oai:hal.archives-ouvertes.fr:hal-00662973 | |
| From: Ying Hu | |
| Submitted on: Wednesday, 25 January 2012 16:23:37 | |
| Updated on: Friday, 27 January 2012 09:33:27 | |
