I am a fourth year Ph.D student at the Department of Statistics under the supervison of Dr.A.Papavasiliou.

My research focuses on the application of rough path theory to statistical problems, including parameter estimation for stochastic differential equations and inverse problem of stochastic differential equations. In general, I am intersted in modeling the continuous process of any roughness and solving relating statistcal problems by a tractable process. I am also interested in fractional stochastic analysis, infinite matrix, graph coloring problems and financial mathematics.

Finished projects

• Algorithm for the calculation of the p-variation of one-dimensional rough paths. An efficient algorithm is derived for the calculation of the p-variation of an one-dimensional rough path by taking the path as a directed acyclic graph (DAG), and applying the topological ordering property.
• Maximum likelihood estimation for the parameters of the discretely observed Ornstein–Uhlenbeck process driven by fractional Brownian motion with 0<H<1. The method is based on the idea of approximating the fractional Ornstein–Uhlenbeck process by a tractable process for which the probability density can be explicitly expressed by the discretely observed data. The weak consistency of the aximum likelihood estimators is proved.

Project in progress

• Inverse problem of stochastic differential equations. Given the discretely observed data from a stochastic system, we want to derive an efficient algorithm to find the driving path. The driving path should be piecewise linear and its reponse from the stochastic system should go through the discrete observations. The algorithm uses the signature of the path as the feature set of the path which is different from the existing algorithms. The direct application relates to my second finished project. It makes the method of parameter estimation apply to stochastic processes with no analytical solutions.

Ph.D Training

• APTS, Statistical Inference and Statistical Computing at Cambridge in Dec, 2014
• APTS, High Dimensional Statistics and Computer Intensive Statistics at Southampton university in Mar, 2015
• Statistic Analysis, 2014
• Brownian Motion, 2015

Seminar and Reading Group

I make regular attendence at the following seminars and reading groups

• Rough path theory reading group
  
• Mathematical finance seminar
• Graph theory seminar

Teaching

• 2017-2018, term 1: ST208 - Mathematical Methods
• 2016-2017, term 2: ST115 - Introduction to Probability
• 2016-2017, term 1: ST208 - Mathematical Methods
• 2015-2016, term 2: ST115- Introduction to Probability
• 2015-2016, term 1: ST208- Mathematical Methods
• 2014-2015, term 2: ST115-Introduction to Probability

Contact Details

University of Warwick, CV4 7AL, Coventry, UK

E-mail: yang.zhao@warwick.ac.uk