Regularity properties for general HJB equations. A BSDE method

In this work we investigate regularity properties of a large class of Hamilton-Jacobi-Bellman (HJB) equations with or without obstacles, which can be stochastically interpreted in form of a stochastic control system which nonlinear cost functional is defined with the help of a backward stochastic differential equation (BSDE) or a reflected BSDE (RBSDE). More precisely, we prove that, firstly, the unique viscosity solution $V(t,x)$ of such a HJB equation over the time interval $[0,T],$ with or without an obstacle, and with terminal condition at time $T$, is jointly Lipschitz in $(t,x)$, for $t$ running any compact subinterval of $[0,T)$. Secondly, for the case that $V$ solves a HJB equation without an obstacle or with an upper obstacle it is shown under appropriate assumptions that $V(t,x)$ is jointly semiconcave in $(t,x)$. These results extend earlier ones by Buckdahn, Cannarsa and Quincampoix [1]. Our approach embeds their idea of time change into a BSDE analysis. We also provide an elementary counter-example which shows that, in general, for the case that $V$ solves a HJB equation with a lower obstacle the semi-concavity doesn't hold true.Comment: 30 page

Appreciation of Meng Haoran’s Chun Xiao and Its English Versions： a Text Linguistic Point of View

Text linguistics, with its ground-breaking theories and methodology, provides readers not only an opportunity to better understand the original text, but also a sound theoretical basis for the appreciation and criticism of its versions. This article thus conducts a study on Meng Haoran’s well-known poem Chun Xiao and its different versions from the perspective of Chinese-English contrastive discourse analysis, taking cohesion and coherence as its major references and criteria. It is aimed to offer some inspiration for the Chinese-English contrastive study as well as translation studies. Key words: text linguistics, English version of Chun Xiao, cohesion, coherence, translation Criticism Résumé: La linguistique du texte est une discipline jeune dont la théorie et la méthode d’analyse aident non seulement le lecteur à mieux comprendre le texte original, mais aussi lui fournir le fondement théorique pour l’appréciation et la critique de la traduction. L’article présent, dans la perspective de l’étude comparative des textes chinois et anglais, en se référant aux deux caractéristiques les plus fondamentales de la linguistique du texte - cohérence et continuité, tente de procéder à des recherches sur le poème L’Aube du printemps de Meng Haoran et ses traductions dans le but d’aider à l’étude comparative des textes chinois et anglais ainsi que les recherches de traduction. Mots-clés: linguistique du texte, version anglaise de L’Aube du printemps, cohérence, continuité, critique de traduction 摘要：語篇語言學是一門新興的學科，其主要理論與分析方法不僅能幫助讀者更好地理解原文，同樣也為其進行譯作的欣賞與批評提供理論基礎。本文擬從漢英語篇對比研究的視角出發，以銜接與連貫這兩個作為語篇語言學最重要的特徵為標準與參照，對孟浩然的《春曉》一詩及其譯本展開嘗試性的探討，目的在於為漢英對比研究與翻譯研究提供一點啟發。關鍵詞：語篇語言學：《春曉》英譯；銜接；連貫；翻譯批