Date/Time : 27 Jun 2018 15:30
Venue : S17 #04-04 SR3
Speaker : Johnson, Liu Qiang , University of Macau

Date/Time:27 Jun 2018 15:30 Venue: S17 #04-04 SR3 Speaker: Johnson, Liu Qiang, University of Macau Inference of Spot Volatility in the presence of Infinite Variation Jumps Empirical evidences witness that the jumps appear to be very frequent in the financial markets. In this talk, we propose a kernel estimator for the spot volatility of an Ito semi-martingale at a given time point by using the high frequency data, under the circumstance that the jumps contained in the underlying driven process could be of infinite variation. The estimator is based on the representation of the characteristic function of Levy processes. The consistency of the proposed estimator is established under some mild assumptions. By assuming that the jump part of the underlying process behaves like a symmetric stable Levy process around 0, we establish the asymptotic normality of the proposed estimator. In particular, with a specific kernel function, the estimator is variance efficient. We conduct Monte Carlo simulation studies to assess our theoretical results. We also extend our theories to the estimation of spot covariation quantities between two Ito semi-martingales. Our estimators are applied to some real high frequency financial data sets for empirical analysis. Add to calendar: 

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Date/Time : 23 May 2018 10:30
Venue : S17 #04-06 SR1
Speaker : Claudia Klüppelberg , Technical University of Munich

Date/Time:23 May 2018 10:30 Venue: S17 #04-06 SR1 Speaker: Claudia Klüppelberg, Technical University of Munich Max-linear models on graphs Graphical models are a popular tool to analyse and visualise dependence properties between random variables; see e.g. Lauritzen (1996). Each node in the graph represents a random variable, and the absence of an edge between two nodes indicates conditional independence between the corresponding random variables. We introduce a new recursive structural equation model, where all random variables can be written as a max-linear function of their parents and independent noise variables. In particular, we define directed graphical models, where edge orientations come along with an intuitive causal interpretation and present conditional independence properties of the model. Furthermore, we use algebraic methods to characterise all max-linear models, which are generated by a structural equation model and detail the relation between the coefficients of the structural equation model (the edge weights of the graph) and the max-linear coefficients. Finally, we extend finite-dimensional max-linear models to models on infinite graphs, and investigate their relations to classical percolation theory, more precisely to nearest neighbour Bernoulli bond percolation. The talk is based on joint work with Nadine Gissibl, Steffen Lauritzen, Moritz Otto, and Ercan Sönmetz. Add to calendar: 

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Date/Time : 26 Apr 2018 15:00
Venue : S17 #04-06 SR1
Speaker : Adam Bowditch , National University of Singapore

Date/Time:26 Apr 2018 15:00 Venue: S17 #04-06 SR1 Speaker: Adam Bowditch, National University of Singapore Trapping mechanisms for random walks on Galton-Watson trees In a range of models of random walks in random environments, the asymptotic behaviour of the walk is driven by a trapping mechanism arising due to adverse regions in the environment. Random walks on trees are a natural example as dead-ends in the tree form traps which slow the walk. In this talk, we discuss biased random walks on both supercritical and subcritical Galton-Watson trees conditioned to survive. In particular, we describe how the trapping observed in these models is influenced by the structure of the tree and focus on questions concerning the existence of a limiting speed, the scale of the fluctuations and the issues concerning functional results. Add to calendar: 

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Date/Time : 29 Mar 2018 15:00
Venue : S17 #04-06 SR1
Speaker : Vadim Gorin , MIT

Date/Time:29 Mar 2018 15:00 Venue: S17 #04-06 SR1 Speaker: Vadim Gorin, MIT Convolutions and fluctuations: free, finite, quantized The talk is about three operations on eigenvalues of self-adjoint matrices obtained from cutting out principal corners, adding and multiplying matrices. We discuss the asymptotic behavior of the operations as the size of the matrix goes to infinity, or as the dimension of the base field (beta parameter) goes to infinity, or in the quantized problem where matrices are replaced by group representations. The first one is classical, the third one is more recent, and the second one is very new. Each case leads to its own operation on measures and its own Gaussian fluctuation field. Add to calendar: 

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Date/Time : 22 Mar 2018 15:00
Venue : S17 #04-06 SR1
Speaker : Andrei Florin Deneanu, Yale University

Date/Time:22 Mar 2018 15:00 Venue: S17 #04-06 SR1 Speaker: Andrei Florin Deneanu, Yale University How often is a random matrix normal? When the matrix entries have a continuous distribution, the probability is zero, as the set of normal matrices, viewed as points in R^{n^2}, is not full dimensional. However, for discrete distributions, the situation is totally different. We are going to focus on the Rademacher matrix, whose entries take values 1 and -1 with equal probabilities and prove an upper bound of 2^{-(0.3+o(1))n^2} for the probability in question. Note also that a lower bound of 2^{-(0.5+o(1))n^2} is given by the fact that every symmetric matrix is normal. Add to calendar: 

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Date/Time : 12 Feb 2018 16:00
Venue : S17 #04-05 SR2
Speaker : Akira Sakai, Hokkaido University

Date/Time:12 Feb 2018 16:00 Venue: S17 #04-05 SR2 Speaker: Akira Sakai , Hokkaido University Hyperscaling for oriented percolation in 1+1 space-time dimensions Consider nearest-neighbor oriented percolation in d+1 space-time dimensions. Let \rho,\eta, \nu be the critical exponents for the survival probability up to time t, the expected number of vertices at time t connected from the space-time origin, and the gyration radius of those vertices, respectively. We prove that the hyperscaling inequality d \nu >= \eta+2\rho, which holds for all d>=1 and is a strict inequality above the upper-critical dimension 4, becomes an equality for d=1, i.e., \nu=\eta+2\rho, provided existence of at least two among \rho,\eta,\nu. The key to the proof is the recent result on the critical box-crossing property by Duminil-Copin, Tassion and Teixeira (2017). Add to calendar: 

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