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[CT075]

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : A Subordinated stochastic process is obtained by time changing a parent process X_t with a positive non-deceasing stochastic process T_t. The process T_t is called the directing process or the random clock. Subordinated processes demonstrate interesting probabilistic properties and have applications in finance, economics, statistical physics, anomalous diffusion and fractional calculus. Also scaling limits of continuous time random walk depending on the conditions on mean waiting times and second moments conditions on jumps converges weakly to different subordinated stochastic process. The aim of this talk is to discuss the concept of subordinated processes and their connections to different fields.
Classification : 60G10, 60G18, 60G20, 62M10, 60G51
Author(s) :
- Arun Kumar (Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab, India 140001)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : In the quest to understand how deep neural networks work, identification of slow and fast variables is a desirable step. Inspired by tools from theoretical physics, in this talk I will present a thermodynamic theory of finite deep neural networks (DNNs) based on two matrix variables per layer. Our theory yields accurate predictions in various settings. In addition, it provides new ways of analyzing and understanding DNNs in the feature learning regime.
Classification : 60G15, 62M45, 62F15, 68T07, 82C31
Author(s) :
- Inbar Seroussi (Tei-Aviv University)
- Gadi Naveh (Hebrew University )
- Zohar Ringel (Hebrew University)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : We consider an optimal stopping problem that addresses \textit{model uncertainty}, which affects the model assumptions, e.g., the parameters embedded in the probability distribution. The result presented in this talk shows the explicit form of the boundary indicating the optimal stopping time, assuming the portfolio value as an Ornstein-Uhlenbeck process. Applying our method might make statistical arbitrage more robust because the trading code for statistical arbitrage often depends on incorrect estimation.
Classification : 60G40, 60G10, 91G80
Author(s) :
- Daisuke Yoshikawa (Kansai University)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : The infinite-server systems driven by Hawkes processes is studied. For the Hawkes/sdHawkes/∞ system, the Markov property of the system is derived. The joint time-dependent distribution of the number of customers in the system, the arrival intensity and the server intensity is obtained. Then, the time-dependent results are also deduced for the M/sdHawkes/∞, Hawkes/M/∞ and M/M/∞ systems.
Classification : 60G55, 60G18, 68M20, 60K30, 60K25
Author(s) :
- Dharmaraja Selvamuthu (Indian Institute of Technology Delhi)
- Paola Tardelli (University of L’Aquila, Piazzale)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : In this talk we investigate geometric properties of random fields on the two-dimensional sphere evolving over time, that are widely used in several scientific areas to model and analyze data (e.g. in Climate Science related to Earth surface temperature). In particular we study the behavior for large time of their excursion area at any threshold, establishing both asymptotic variances and limit theorems. We will show that phase transitions can occur for specific levels and memory.
Classification : 60G60, 33C55, 60D05, 60F05, 62M15
Author(s) :
- Domenico Marinucci (University of Roma "Tor Vergata")
- Maurizia Rossi (University of Milano-Bicocca)
- Anna Vidotto (University of Napoli "Federico II")