About:
The next KE Hub online Triage Workshop will be presented by Moody's Analytics.
Limit laws for stochastic cumulative transition matrices
Let X= (X(t): t=1,…,T) denote a discrete Markov chain of N×N complex matrices, where X(1),…,X(T) are not necessarily independent or identically distributed. What can we say about the distribution of the eigenvectors and eigenvalues of Y(T)=X(1)X(2)…X(T)? For example, under what conditions can we expect a Central Limit Theorem-type result to hold for log(Y(T))/T as T tends to infinity?
The question is motivated by the need to understand the distribution of:
- cumulative transition matrices in credit models where the one-period stochastic transition matrices are serially correlated;
- cumulative conditional transition matrices where the conditioning variables are stochastic and serially correlated.
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Academic mathematical scientists from KE Hub partner university departments are invited to take part in these workshops. If you would like to attend, please contact your local KE Champion to receive the meeting link or get in touch with the organisers, Lauren Hyndman and Diwei Zhou.
KE Hub Triage Workshops are informal discussion sessions where one B.I.G. Partner presents a challenge they are currently facing, with the aim of determining:
- What, if any, mathematical sciences approaches can be used to address the challenge?
- Who from the mathematical sciences community would like to take on the challenge?
- What mechanisms are most appropriate for driving the challenge forward?
The purpose of these workshops is to allow the B.I.G. Partner to engage directly with academic mathematical scientists to probe the scientific content of their proposed challenge. The environment is relaxed and interactive, and we encourage questions, clarifications and discussions throughout. You can find information on all upcoming and past workshops here.