2019年度

場所/Place: 関西大学第4学舎1号館 1301教室/Kansai University, 4th School Area, 1st Buld., R1301

時間/Time: 15:00 -- 16:30

講演者/Speaker: 上原 悠槙 氏 (統計数理研究所)/ Yuma UEHARA (The Institute of Statistical Mathematics)

講演題目/Title: Bootstrap Gaussian maximum quasi-likelihood estimator for misspecified ergodic SDE models

講演要旨/Abstract: エルゴード的確率微分方程式からの高頻度観測に基づくガウス型擬似最尤推定量は、 収束レートの差異はあれど様々な分布特性を持つ駆動ノイズに対して機能する。 しかし、想定する統計モデルが誤特定された下では、 当該推定量の漸近分散には誤特定バイアス補正に伴うポテンシャル関数が現れる。 これにより、漸近分散の一致推定量を得ることが困難となる。 本講演ではこの問題に対し、ブロック和に対するブートストラップ型の推定量を構築し、 それが元の推定量の漸近分布の近似量となっていることを示す。


場所/Place: 関西大学第4学舎1号館 1301教室/Kansai University, 4th School Area, 1st Buld., R1301

時間/Time: 14:40 -- 16:10 (I)

講演者/Speaker: Velleret Aurélien (Aix Marseille Université, France)

講演題目/Title: Generalization of Harris recurrence to Feynman-Kac models with some applications to eco-evolutionary dynamics.

講演要旨/Abstract: I shall present a way to tackle the issue of the long-time behavior of a stochastic process biased in some Feynman-Kac representation. With the assumptions I propose, we can deduce the quasi-ergodicity of the model. It includes notably the exponential convergence in total variation of the marginals to a unique quasi-stationary distribution, and the convergence of the empirical average to a unique quasi-ergodic distribution. The foundation of the proof is the time-inhomogeneous version of Harris recurrence, so the technique does not rely on any reversibility condition and can be applied to space- and time-continuous processes. A specific focus is laid on models with a non-uniform convergence and discontinuous trajectories. In models of eco-evolutionary dynamics, such Feynman-Kac representation is naturally derived from the description of a « typical » individual when death and repoduction events take place. There are also promising applications from Large Deviation theory.

講演者/Speaker: 金 大弘 氏(熊本大学工学部)/Daehong KIM (Kumamoto University)

講演題目/Title: Scattering length of positive potentials and applications.

講演要旨/Abstract: In this talk, we study the scattering length for positive additive functionals of symmetric stable processes on a d-dimensional Euclidean space. The additive functionals considered here are not necessarily continuous. We shall consider the semi-classical asymptotic problems for the scattering length of positive potentials. We also consider, as an application, certain equivalent criterion for the fractional Laplacian with a measure valued non-local operator as a perturbation to have purely discrete spectrum in terms of the scattering length.


場所/Place: 関西大学第4学舎1号館3階1302教室/Kansai University, 4th School Area, 1st Buld., R1302

時間/Time: 15:40 -- 17:10

講演者/Speaker: 田口 大 氏 (大阪大学大学院基礎工学研究科)/ Dai TAGUCHI (Osaka Univ.)

講演題目/Title: Probability density function of SDEs with unbounded and path--dependent drift coefficient

講演要旨/Abstract: In this talk, we prove that the existence and Gaussian two-sided bound for a probability density function of a solution of SDEs with unbounded and path-dependent drift coefficient. We also provide two explicit representations for the density. The first representation is an analogue of Levi's parametrix method and the second representation is related to Maruyama's proof of Girsanov Theorem. The idea of the proof is to use "local" Novikov condition and Maruyama-Girsanov transformation. As an application of explicit representation, we provide the rate of convergence for the Euler--Maruyama approximation. This talk is based on joint work with Akihiro Tanaka.


場所/Place: 関西大学第4学舎1号館2階数学科実験実習室/Kansai University, 4th School Area, 1st Buld., Mathematics Seminar Room

時間/Time: 15:00 -- 16:00

講演者/Speaker: 濱名 裕治 氏 (熊本大学)/ Yuji HAMANA (Kumamoto Univ.)

講演題目/Title: The transition densities of radial symmetric stable processes