Probability Seminar, Department of Mathematics & Statistics
Probability Seminar, Department of Mathematics & Statistics
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Michael Grabchak

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Wed March 10, 2020 at 4:00PM in Fretwell 379 (Math Conference Room)

March 10, 2020 by Michael Grabchak
Categories: Probability Seminar

Stanislav Molchanov, UNC Charlotte

Title: An Introduction to Markov Dynamics

Wed Feb 19, 2020 at 4:00PM in Fretwell 379 (Math Conference Room)

February 18, 2020 by Michael Grabchak
Categories: Probability Seminar

Stanislav Molchanov, UNC Charlotte

Title: Random Permutations and Dickman’s Law Part 3

Wed Feb 12, 2020 at 4:00PM in Fretwell 379 (Math Conference Room)

February 06, 2020 by Michael Grabchak
Categories: Probability Seminar

Stanislav Molchanov, UNC Charlotte

Title: Random Permutations and Dickman’s Law Part 2

Wed Feb 5, 2020 at 4:00PM in Fretwell 379 (Math Conference Room)

February 03, 2020 by Michael Grabchak
Categories: Probability Seminar

Stanislav Molchanov, UNC Charlotte

Title: Random Permutations and Dickman’s Law

Wed Nov 20, 2019 at 5:30PM in Fretwell 379 (Math Conference Room)

November 18, 2019 by Michael Grabchak
Categories: Probability Seminar

Isaac Sonin, UNC Charlotte

Title: Nonhomogeneous Markov Chains and O-1 Laws

Wed Nov 5, 2019 at 5:30PM in Fretwell 379 (Math Conference Room)

November 05, 2019 by Michael Grabchak
Categories: Probability Seminar

Stanislav Molchanov, UNC Charlotte

Title: Several problems on infinitely divisible distributions

Fri Nov 1, 2019 at 3:00PM in Fretwell 315

October 30, 2019 by Michael Grabchak
Categories: Probability Seminar

Ion Grama, University of South Brittany

Title: Conditioned limit theorems for products of random matrices and Markov chains with applications to branching processes.

Abstract: Consider a random walk defined by the consecutive action of independent identically distributed random matrices on a starting point outside the unit ball in the d dimensional Euclidean space. We study the first moment when the walk enters the unit ball. We study the exact behavior of this time and prove conditioned limit theorems for the associated Markov walk. This extends to the case of walks on group GL(d,R) the well known results by Spitzer. The existence of the harmonic function related to the Markov walk turns out to be a crucial point of the proof. We have extended these results to general Markov chains and applied them to study the branching processes in Markov environment.

Wed Oct 23, 2019 at 5:30PM in Fretwell 379 (Math Conference Room)

October 21, 2019 by Michael Grabchak
Categories: Probability Seminar

Isaac Sonin, UNC Charlotte

Title: A Continuous-Time Model of Financial Clearing Part 2

Abstract: We present a simple model of clearing in financial networks in continuous time. In the model, banks (firms, agents) are represented as tanks (reservoirs) with liquid (money) flowing in and out. This approach provides a simple recursive solution to a classical static model of financial clearing introduced by Eisenberg and Noe (2001). It also suggests a practical mechanism of simultaneous and real time payments. The dynamic structure of our model helps answer other related questions and, potentially, opens the way to handle more complicated dynamic financial networks, e.g., liabilities with different maturities. Also, our approach provides a useful tool for solving nonlinear equations involving a linear system and max min operations similar to the Bellman equation for the optimal stopping of Markov chains and other optimization problems.

Wed Oct 16, 2019 at 5:30PM in Fretwell 379 (Math Conference Room)

October 12, 2019 by Michael Grabchak
Categories: Probability Seminar

Isaac Sonin, UNC Charlotte

Title: A Continuous-Time Model of Financial Clearing Part 1

Abstract: We present a simple model of clearing in financial networks in continuous time. In the model, banks (firms, agents) are represented as tanks (reservoirs) with liquid (money) flowing in and out. This approach provides a simple recursive solution to a classical static model of financial clearing introduced by Eisenberg and Noe (2001). It also suggests a practical mechanism of simultaneous and real time payments. The dynamic structure of our model helps answer other related questions and, potentially, opens the way to handle more complicated dynamic financial networks, e.g., liabilities with different maturities. Also, our approach provides a useful tool for solving nonlinear equations involving a linear system and max min operations similar to the Bellman equation for the optimal stopping of Markov chains and other optimization problems.

Wed Sept 25, 2019 at 5:30PM in Fretwell 379 (Math Conference Room)

September 30, 2019 by Michael Grabchak
Categories: Probability Seminar

Stanislav Molchanov, UNC Charlotte

Title: Discrete Dynamo Part 4

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