10th World Congress in Probability and Statistics
Contributed Session (live Q&A at Track 2, 9:30PM KST)
Financial Mathematics and Probabilistic Modeling
Solving the selection-recombination equation: ancestral lines and duality
Frederic Alberti (Bielefeld University)
We consider the case of an arbitrary number of neutral loci, linked to a single selected locus. In this setting, we investigate how the (random) genealogical structure of the problem can be succinctly encoded by a novel `ancestral initiation graph', and how it gives rise to a recursive integral representation of the solution with a clear, probabilistic interpretation.
-F. Alberti and E. Baake, Solving the selection-recombination equation: Ancestral lines under selection and recombination, https://arxiv.org/abs/2003.06831
-F. Alberti, E. Baake and C. Herrmann, Selection, recombination, and the ancestral initiation graph, https://arxiv.org/abs/2101.10080
Short time asymptotics for modulated rough stochastic volatility models
Barbara Pacchiarotti (Università degli studi di Roma "Tor Vergata")
How to detect a salami slicer: a stochastic controller-stopper game with unknown competition
Kristoffer Lindensjö (Stockholm University)
Q&A for Contributed Session 02
Hyungbin Park (Seoul National University)
SDEs and Fractional Brownian Motions
Weak rough-path type solutions for singular Lévy SDEs
Helena Katharina Kremp (Freie Universität Berlin)
Functional limit theorems for approximating irregular SDEs, general diffusions and their exit times
Mikhail Urusov (University of Duisburg-Essen)
(1) A functional limit theorem (FLT) for weak approximation of the paths of arbitrary continuous Markov processes;
(2) An FLT for weak approximation of the paths and exit times.
The second FLT has a stronger conclusion but requires a stronger assumption, which is essential. We propose a new scheme, called EMCEL, which satisfies the assumption of the second FLT and thus allows to approximate every one-dimensional continuous Markov process together with its exit times. The approach is illustrated by a couple of examples with peculiar behavior, including an irregular SDE, for which the corresponding Euler scheme does not converge even weakly, a sticky Brownian motion and a Brownian motion slowed down on the Cantor set.
This is a joint work with Stefan Ankirchner and Thomas Kruse.
Q&A for Contributed Session 07
Ildoo Kim (Korea University)
Neural Networks and Deep Learning
Simulated Annealing-Backpropagation Algorithm on Parallel Trained Maxout Networks (SABPMAX) in detecting credit card fraud
Sheila Mae Golingay (University of the Philippines-Diliman)
The smoking gun: statistical theory improves neural network estimates
Sophie Langer (Technische Universität Darmstadt)
Stochastic block model for multiple networks
Tabea Rebafka (Sorbonne Université)
Deep neural networks for faster nonparametric regression models
Mehmet Ali Kaygusuz (The Middle East Technical University)
 Bauer, B and Kohler,M, “On deep learning as a remedy for the curse of dimensionality in nonparametric regression”, The Annals of Statistics, 47(4), 2019, 2261-2285.
 Efron,B, "Bootstrap methods: another look at the jackknife" the Annals of Statistics,7(1):1-26,1979
 Hamparsum Bozdogan. “Model selection and Akaike’s information criterion (AIC): The general theory and its analytical extensions”. In: Psychometrika 52.3 (1987), pp. 345–370.
 Sen,B, Banerjee, M and Woodroofe,M., “In-cosistency of bootstrap: The Grenander estimator ”, The Annals of Statistics,38(4),2010,1953-1977.
 Schmidt-Hieber, J., “Nonparametric regression using deep neural networks with ReLu activation function”, The Annals of Statistics, 48(4), 2020, 1875-1897.
Generative model for fbm with deep ReLU neural networks
Michael Allouche (Ecole Polytechnique)
Q&A for Contributed Session 28
Jong-June Jeon (University of Seoul)