Stochastic processes and applications

我通过开发新的模型和算法来解决社会和经济上重要的问题。我过去的研究对几家公司产生了积极的影响，导致了一个专利奖和另外三个专利申请（都是由合作公司提出的），为我赢得了CBS节目“数字”的咨询职位，并为我赢得了2001年PIMS全国推广奖。未来的计划包括通过冰芯样本研究气候变化，通过最佳检测威胁和瓶颈来改进网络，通过最佳选择广告和分类观众来解决有针对性的广告问题，以及通过跟踪潜艇和污染来保护水域。与这些目标相关的一些数学创新包括发展滤波理论，这些理论可以处理重尾过程，支持已经建立的鲁棒实现，从单纯（部分微分方程定义）轨迹和观察中估计信号，这些信号是根据复杂的点过程、马尔可夫链和随机环境定义的，而不是存在噪声设置的通常扭曲的信号。在每个应用程序中，我都与致力于感兴趣领域的公司或个人合作。

I solve socially and economically important problems by developing novel models and algorithms. My past research has affected several companies positively, resulted in one patent award with three more filings (all by partner companies), earned me a consulting role with CBS show `Numbers', and won me the 2001 PIMS national outreach award. Future plans include studying climate change through ice core samples, improving the network by detecting threats and bottlenecks optimally, solving targeted advertizing by optimally selecting ads and classifying viewership and securing waters by tracking submarines and pollution. Some mathematical novelties associated with these goals include developing filtering theories that can handle heavy-tailed processes, support robust implementations beyond those already established, estimate signals from mere (partial-differential-equation-defined) traces and observations that are defined in terms of complicated point processes, Markov chains and random environments instead of the usually distorted signal in presence of noise setting. In every application, I work with corporations or individuals dedicated to the area of interest.