主题：Fractional Brownian motion and its applications in finance and other fields（分数布朗运动及其在金融等领域的应用）
报告人：Elena Issoglio, 意大利人，伦敦国王学院讲师、博士后。毕业于德国耶拿大学和英国曼彻斯特大学，获得数学博士学位。2008年至2012年为欧盟玛丽居里初级人才培养计划初级研究员。
These notes are devoted to fractional Brownian motion (fBm) and its applications. FBm is a family of Gaussian processes which has the interesting property of having dependent increments, in particular, its increments can exhibit long-range dependence. Moreover it is self-similar. Thanks to these properties, fBm can be applied as a model in many fields, such as finance, neurobiology, physics or telecommunications.
In these notes, after a brief introduction to probability theory and stochastic processes, we define fBm and describe its many features. We then present in detail a theory of stochastic integration with respect to fBm which is suitable for deterministic integrands (Wiener integral) and we give an insight to some of the possible extensions to stochastic integrands. Finally we present several examples in different fields where fBm can be applied as suitable source of noise.