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的重要问题。我过去的研究对几家公司产生了积极的影响，导致了一项专利奖和三项专利申请（全部由合作伙伴公司提交），为我赢得了哥伦比亚广播公司节目“数字”的咨询角色，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善网络，通过最佳选择广告和分类观众来解决有针对性的广告，通过跟踪潜艇和污染来保护沃茨。与这些目标相关的一些数学创新包括开发可以处理重尾过程的滤波理论，支持超出已经建立的鲁棒实现，仅从（偏微分方程定义的）轨迹和观测中估计信号，这些轨迹和观测是根据复杂的点过程，马尔可夫链和随机环境定义的，而不是在存在噪声设置的情况下通常失真的信号。在每一个应用程序中，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.