Stochastic processes and applications

我通过开发新的模型和算法来解决重要的社会和经济问题。我过去的研究对几家公司产生了积极的影响，获得了一项专利奖，又提交了三份申请(都是由合作伙伴公司提交的)，为我赢得了CBS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，通过优化检测威胁和瓶颈来改善网络，通过优化选择广告和对收视率进行分类来解决定向广告，通过跟踪潜艇和污染来确保水域安全。与这些目标相关的一些数学新颖性包括开发可以处理重尾过程的滤波理论，支持在已建立的滤波理论之外的稳健实现，从仅根据复杂的点过程、马尔可夫链和随机环境定义的轨迹和观测来估计信号，而不是在存在噪声的情况下通常失真的信号。在每一份申请中，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.