主题： Characterising the path-independence of stochastic differential equations: a problem arising in financial modelling
This talk will address a problem arising in financial modelling with stochastic differential equations (SDEs). A characterisation theorem will be derived in which we establish a new link from SDEs to nonlinear parabolic PDEs. Starting from the necessary and sufficient conditions of the path-independence of the density of Girsanov transform for SDEs, we are able to derive a characterisation by means of nonlinear parabolic equations of Burgers-KPZ type. Extensions to the cases of degenerated SDEs, jump SDEs, as well as to (infinite dimensional) SDEs on separable Hilbert spaces will be discussed. A perspective to stochastically deformed dynamical systems will be briefly considered.
讲述人简介：吴奖伦，英国斯旺西大学(Swansea University)传授，华中科技大学数学中央外洋客座传授。吴奖伦传授在《Stochastic Process. Appl.》, 《J. Funct. Anal. 》, 《Trans. Amer. Math. Soc. 》, 《Potential Anal.》，《Bull. Sci. Math. 》等国际威望期刊上揭晓学术论文80多篇. 其研讨范畴包罗：随机剖析、非尺度剖析和无限维剖析；研讨题目包罗：数学物理、特别构造量子场和统计力学等学科中与概率论相干的无限维剖析题目.