A PROBABILISTIC APPROACH TO THE GENERALIZED HESSIAN

• 成果类型: Article
• 署名作者: HAUSSMANN, UG
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.17.2.411
• 发表日期: 1992
• 页码: 411-443
• 关键词: 2nd-order

摘要

The quadratic variation of Brownian motion is used to give a new definition of a generalized Hessian for nonsmooth functions, totally independently of any gradients. A calculus is developed for the generalized Hessian of functions whose gradient is Lipschitz. It is also shown that for convex functions the Hessian is nonempty.