# List of Talks

**Title: ***Uniform limit theorems for point processes*

**Abstract:** "We study the asymptotic behavior of a sequence of i.i.d. point processes

over a class of bounded measurable functions. Specifically, under suitable

measurability and moment assumptions, we provide sufficient conditions for

the uniform law of large numbers (LLN) and the uniform central limit the-

orem in terms of random metric entropy. Additionally, we establish the

uniform rates of convergence for the LLN. These results directly apply to

sequences of tree-indexed random variables, which may be dependent if they

share a common parent vertex. As a consequence, we obtain uniform consis-

tency and uniform asymptotic normality for Lotka-Nagaev and Harris-type

estimators for functionals of tree-indexed random variables. Furthermore, we

derive the uniform asymptotics properties of halfspace depth allowing an in-

quiry concerning medians and quantiles of tree-indexed multivariate random

variables."

**References: **[1] G. Francisci and A. N. Vidyashankar. Functional limit laws for the in-

tensity measure of point processes and applications. 2024+.

Institute of Mathematical Finance, Ulm University

**Title:** *Optimal tests for the absence of random individual effects in large "n" and small "T" dynamic panels*

**Abstract:**

This is joint work with Nezar Bennala and Marc Hallin (Université libre de Bruxelles)."

Kyushu University

Fukuoka, Japan

**Title:** *Minkowski functionals for non-Gaussian orthogonally invariant random fields on spheres*

**Abstract**: "The Minkowski functionals are statistics for capturing morphological features, typically in 2 or 3-dimensional images.

In particular, in astrophysics, it has been used to gasp non-Gaussian information in the large-scale structure of the Universe,

the CMB, and so on. With such applications in mind, in our previous work, we have obtained the asymptotic expansion formulas

for the expected Minkowski functionals for weakly non-Gaussian isotropic random fields (i.e., central limit random fields) in

arbitrary dimensional Euclidian space. In this talk, we consider non-Gaussian orthogonally invariant random fields on spheres.

The CMB is regarded as a restriction of a 3-dimensional isotropic random field to a 2-dimensional sphere, hence orthogonally

invariant. We present the expected Minkowski functional formula for non-Gaussian random fields including Gaussian, Chi-square,

and weakly non-Gaussian random fields. We also discuss how restrictive an orthogonally invariant random field is if it

is defined as a restriction to an isotropic random field on higher dimensional Euclidean space.

This is joint work with Takahiko Matsubara (High Energy Accelerator Research Organization (KEK))."

The Institute of Statistical Mathematics

ISM

Tokyo, Japan

**Title: ***Causal Inference for Random Objects*

**Abstract**: "Adjusting for confounding and imbalance when establishing statistical relationships is an increasingly important task, and causal

inference methods have emerged as the most popular tool to achieve this. Causal inference has been developed mainly for scalar

outcomes and recently for distributional outcomes. We introduce here a general framework for causal inference when outcomes

reside in general geodesic metric spaces, where we draw on a novel geodesic calculus that facilitates scalar multiplication for

geodesics and the characterization of treatment effects through the concept of the geodesic average treatment effect. Using ideas

from Frechet regression, we develop estimation methods of the geodesic average treatment effect and derive consistency and

rates of convergence for the proposed estimators. We also study uncertainty quantification and inference for the treatment effect.

Our methodology is illustrated by a simulation study and real data examples for compositional outcomes of U.S. statewise energy

source data to study the effect of coal mining, network data of New York taxi trips, where the effect of the COVID-19 pandemic is of

interest, and brain functional connectivity network data to study the effect of Alzheimer's disease."

University of Tokyo

Tokyo, Japan

**Title: ***Outlier-resistant inference without jump-detection filter*

**Abstract:** "We propose a modified Gaussian quasi-likelihood through density-power weighting. It is designed for estimating the

continuous part of a stochastic process in the presence of jump-type and/or spike-type outliers. We will present the

asymptotic distributional properties of the proposed estimator, followed by illustrative simulation results which show

how much the estimator is robust against outliers and is sensitive to (one-parameter) fine-tuning."

University of Tokyo

Tokyo, Japan

**Title: **Stochastic 3D modeling of the nanoporous binder-additive phase in battery electrodes

**Abstract**: "A stochastic 3D model for the nanoporous binder-additive phase in hierarchically structured

electrodes of lithium-ion batteries is presented. The considered binder-additive phase consists

of carbon black, polyvinylidene difluoride binder and graphite particles. For stochastic 3D mod-

eling, we use a three-step approach combining excursion sets of Gaussian random fields with

germ-grain models. First, the graphite particles extracted from image data are modeled by a

Boolean model with ellipsoidal grains. Second, the union of carbon black and binder is mod-

eled by an excursion set of a Gaussian random field in the complement of the graphite particles.

Third, large pore regions within the union of carbon black and binder are modeled by a Boolean

model with spherical grains. The model is calibrated to tomographic image data of cathodes

in lithium-ion batteries acquired by focused ion beam scanning electron microscopy. Subse-

quently, model validation is performed by comparing various morphological descriptors, that

are not used for model fitting, of both model realizations and measured image data. Moreover,

we use the validated model for generating virtual, yet realistic, image data of the nanoporous

binder-additive phase with systematic variations in the volume fraction of graphite particles.

The latter can be controlled by adjusting the intensity of the Boolean model with ellipsoidal

grains. Based on this virtual analysis, we quantitatively study the influence of graphite parti-

cles on morphological descriptors as well as on effective transport properties such as effective

conductivity in the binder-additive phase and effective diffusivity in the pore space.

This is joint work with Phillip Gräfensteiner und Volker Schmidt (Ulm University)."

Institute of Statistics, Graz University of Technology

Graz, Austria

**TItel: ***Efficient drift parameter estimation for ergodic solutions of backward SDEs*

**Abstract**: "This study addresses the problem of asymptotically efficient estimation of

drift parameters in ergodic backward stochastic differential equations (BSDEs).

Unlike previous studies that assumed known or parametric models for the diffusion

coefficient, we consider a more general setting where the diffusion coefficient is

unknown and nonparametric. We propose a maximum likelihood-type estimator

based on discrete observation data and prove its consistency and asymptotic normality.

Furthermore, we demonstrate that the proposed method achieves the optimal asymptotic

variance attainable when the diffusion coefficient is observable. This enables efficient

parameter estimation even in models with unknown stochastic volatility. To complement

the theoretical results, we also conducted numerical experiments to confirm the effectiveness

of the proposed method. The findings of this research are expected to contribute to various

fields where BSDEs are applied, such as the analysis of stochastic volatility models in

financial engineering and optimal control problems.

This is joint work with Mitja Stadje (Ulm University)."

University of Tokyo, Japan

Tokyo, Japan

**Title: **Investigating the aging behavior of anodes in solid-oxide fuel cell using stochastic 3D microstructure modeling based on excursion sets of Gaussian random fields

**Abstract: **"Solid oxide fuel cells (SOFCs) are becoming increasingly important due to their high electrical

efficiency, the flexible choice of fuels and relatively low emissions of pollutants. However, the increasingly

growing demands for electrochemical devices require further performance improvements as for example

by reducing degradation effects. Since it is well known that the 3D structure of the electrodes has a profound

impact on the resulting performance, a deeper understanding of process-structure-property relationships is

required. Since tomographic imaging is time-consuming and cost-intensive, virtual materials testing is a

promising approach to tackle this issue by generating a large number of virtual, but realistic microstructures

drawn from a stochastic 3D microstructure model. In this talk, we present the calibration of such a model to

image data, which is segmented into gadolinium-doped ceria (GDC), nickel and pore space [1]. More precisely,

the pluri-Gaussian model described in [2] is calibrated to three-phase microstructures obtained by a numerical

aging simulation [3]. Since one and the same model type is used for each aging scenario, interpolation within

the parameter space allows for predicting the 3D microstructure of SOFC anodes for aging conditions, for

which no tomographic image data is available.

^{[1] S. Weber, B. Prifling, M. Juckel, Y. Liu, M. Wieler, A. Weber, N. Menzler, V. Schmidt, Comparing the 3D morphology of solid-oxide fuel cell anodes for different manufacturing processes, aging durations, and operating temperatures. Working paper (under preparation). [2] M. Neumann, M. Osenberg, A. Hilger, D. Franzen, T. Turek, I. Manke, V. Schmidt, On a pluri-Gaussian model for three-phase microstructures, with applications to 3D image data of gas-diffusion electrodes. Computational Materials Science 156 (2019), 325-331. [3] S. Weber, B. Prifling, R. K. Jeela, D. Schneider, B. Nestler, V. Schmidt, Quantitative investigating the aging behavior of anodes in solid-oxide fuel cells by combining stochastic 3D microstructure modeling with physics-based aging simulations. Working paper (under preparation)}."

Ulm University, Institute of Stochastics

Germany

**Title: **On construction of Markov chains with given dependence and marginal stationary distributions

**Abstract: **A method of constructing Markov chains on finite state spaces is provided. The chain is specified by three constraints:

stationarity, dependence and marginal distributions. The generalized Pythagorean theorem in information geometry

plays a central role in the construction. Integer-valued autoregressive processes are considered for illustration.

University of Tokyo, Japan

Tokyo, Japan

**TItle**: *On Whittle estimation for Levy continuous-time moving average process*

**Abstract:** "In this talk, we consider the estimation problem of Levy continuous-time moving

average process with memory property. We utilize Whittle likelihood function in order to

estimate the parameter in the kernel. We present the asymptotic behavior of the estimator

and related numerical result."

Kansai University, Japan

**TItle:** *The Geometry of Time-Dependent Spherical Random Fields*

**Abstract:**"In this talk, we consider fluctuations over time for the area of the excursion sets

and the length of level curves of time-dependent Gaussian spherical random fields. We focus

on both long and short memory assumptions; in the former case, we show that the fluctuations

are dominated by a single Wiener chaotic component and the existence of cancellation levels

where the variance is asymptotically of smaller order. In the short memory case, we show

that all Wiener chaoses contribute in the limit, no cancellation occurs and a Central Limit

Theorem can be established by Breuer-Major type arguments. The talk is based on two articles

written together with Domenico Marinucci and Maurizia Rossi."

University of Naples Federico II, Italy

Naples, Italy

**Title:** *A stochastic 3D microstructure model for loam and sand based on Gaussian random fields*

**Abstract: **"The 3D microstructure of soils crucially influences the growth of plants and, especially,

the organization of plant roots. Nutrient availability and uptake are key factors of plant growth

which are specifically linked to the pore space morphology of soil. More precisely, diffusive

processes within the pore space need to be further investigated to better understand the relationship

between soil morphology and plant root organization. As experimental investigation of diffusion is

costly and time-consuming, numerical methods for simulating transport have emerged. Numerical

simulations on tomographic image data combined with the assessment of geometrical descriptors

have been used to investigate the relationship between pore space morphology and soil gas diffusion [1].

However, different types of soil are extremely heterogeneous and thus, considering only limited amounts

of measured image data may not be sufficient for a thorough investigation. In this talk, we present a

stochastic 3D microstructure model for different types of soil which is based on excursion sets of

Gaussian random fields [2]. Using this model, we obtain a wide variety of simulated, yet realistic soil

structures which form the basis for further investigations."

^{[1] B. Prifling, M. Weber, N. Ray, A. Prechtel, M. Phalempin, S. Schlüter, D. Vetterlein, V. Schmidt, Quantifying the impact of 3D pore space morphology on soil gas diffusion in loam and sand. Transport in Porous Media 149 (2023), 501-527.}

^{[2] M. Weber, B. Prifling, N. Ray, A. Prechtel, M. Phalempin, S. Schlüter, D. Vetterlein, V. Schmidt, Investigating relationships between 3D pore space morphology and soil gas diffusion based on data-driven spatial stochastic modeling. Working paper (under preparation).}

Ulm University, Germany