Rare events

在金融、制造业和电信等领域，罕见的事件会发生，往往会带来灾难性的后果。一种罕见的事件可能是在短时间内大量索赔导致保险公司破产，或者出人意料的高分组到达率可能导致电信系统中的缓冲区过载。稀有事件很难精确模拟，因为感兴趣的事件很少发生。建议是计算特定大偏差的概率，并找到最可能的路径。这两条信息可以帮助重新设计一个系统，以降低这种罕见事件的可能性。特别令人感兴趣的是大偏差，其中最可能的路径是非线性的；即，有时会出现这样的情况，即系统的另一部分中的罕见事件会使其故障级联整个网络。最近提出的一种近似时间反转的想法似乎是解决这些非线性问题的关键。申请人希望将这些方法应用于金融(R.Nikzad正在研究一个与加拿大银行相关的问题)、罕见事件模拟(杰西·科林伍德正在攻读工程学罕见事件博士学位)和电信领域。

Rare events arise, often with catastrophic consequences, in fields such as finance, manufacturing and telecommunications. A rare event might be large number of claims in a short period of time bankrupting an insurance company or an unexpectedly high rate of packet arrivals may cause a buffer overload in a telecommunications system. Rare events are difficult to simulate precisely because the event of interest occurs so rarely. The proposal is to calculate the probability of particular large deviations, and find the most probable path. These two pieces of information can help redesign a system to make the rare event even less likely. Of particular interest are large deviations where the most probable path is nonlinear; i.e. it is sometimes the case that one gets sideswiped by a rare event in another part of the system whose failure cascades across the network. A recent idea of an approximate time reversal seems to be the key to solving these nonlinear problems. The applicant hopes to apply these methods to finance (R. Nikzad is working on a problem relevant to the bank of Canada) to rare event simulation (Jesse Collingwood is doing his Ph.D. on rare events in engineering) and to telecommunications.