必赢中-俄概率论及其应用研讨会

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必赢中-俄概率论及其应用研讨会

主讲人1

姓 名

Alexander

Shklyaev

所在单位

莫斯科大学

职称/职务

高级研究员

简历

Alexander Shklyaev自2002年本科进入世界知名的莫斯科大学后于2011年在该校获得博士学位并留校工作至今，现为莫斯科大学力学与数学学院高级研究员。研究方向为随机环境中的分枝过程、大偏差理论、卡方检验和统计应用等，在知名国际期刊Theory of Probability and Its Applications, Discrete Mathematics and

Applications, Journal of Mathematical Sciences等发表20余篇sci论文。

报告题目

Limit Theorem for Markov Linear Recurrence Sequences in a Random Environment

报告

主要观点

In the talk we will discuss limit theorems for MLRSRE. The main results for BPRE-such as normal deviations, non-extinction probabilities in different regimes (critical, subcritical), extinction of a population with a large initial number of particles, upper large deviations, lower large deviations, functional limit theorems-can be proved for MLRSRE under general conditions.

主讲人照片

主讲人2

姓 名

Alexey Khartov

所在单位

俄罗斯科学院哈尔科维奇信息传输问题研究所

职称/职务

高级研究员

简历

Alexey Khartov 2008年在莫斯科国立通讯与信息技术大学获得学士学位，2012年在圣彼得堡国立大学获得硕士学位，2014年在圣彼得堡斯捷克洛夫数学研究所（俄罗斯科学院）获得博士学位，现为俄罗斯科学院哈尔科维奇信息传输问题研究所高级研究员。研究方向为无穷可分分布、极限定理、多变量随机过程逼近等。在Electron. J.

Probab., Bernoulli, Theory Probab. Appl., Pacific Journal of Math

ematics等国际知名期刊发表论文30多篇。

报告题目

On rational-infinitely divisible distributions

报告

主要观点

In the talk, we will consider a new class of so-called rational-infinitely (or quasi-infinitely) divisible probability laws. The characteristic functions of  distributions of this class are ratios of the characteristic functions of classical infinitely divisible laws and they admit Lévy-Khinchine representations with signed spectral measures. This class is rather wide and it has nice properties. So criteria of belonging to this class are of interest. Old and new results in this area will be discussed in the talk. In addition, we will present a solution for an open problem formulated by K. Sato and his co-authors on the decomposition of rational-infinitely divisible laws. The results complement the theory of decompositions of distributions developed in the works by Lévy, Khinchine, Linnik, and others.

主讲人照片

主讲人3

姓 名

Pavel Gumenyuk

所在单位

米兰理工大学

职称/职务

副教授

简历

Pavel Gumenyuk 2005年博士毕业于俄罗斯萨拉托夫国立大学，先后挪威、西班牙、意大利、挪威从事博士后、研究院、访问（副）教授和访问教授，现为意大利米兰理工大学数学系副教授。研究方向为复分析、全纯动力系统、几何函数论、Loewner理论与随机过程等。在国际著名期刊Mathematische Annalen, Trans. Amer. Math. Soc., J. Geom. Anal., J. Lond. Math. Soc, Internat. J. Math.等发表论文36篇，为Transactions of the American Mathematical Society等近30个国际学术期刊的审稿人。在西班牙、瑞典、德国、挪威、意大利、芬兰、日本等国家长期进行学术访问与交流，获得了俄罗斯、挪威、西班牙、意大利等国家的荣誉和奖项。

报告题目

Holomorphic dynamics, Loewner Theory, and time-inhomogeneous branching processes

报告

主要观点

At the beginning of the talk, we present a brief introduction to the iteration theory of holomorphic self-maps of a simply connected domain in the complex plane, both in case of discrete and continuous time. In Probabilities, iteration of holomorphic self-maps is classically known to arise naturally in the study of homogeneous branching processes. The non-autonomous holomorphic dynamical systems, which in the probabilistic context correspond to inhomogeneous branching processes, are studied in the so-called Loewner Theory, originated from an attempt to solve Bieberbach’s famous problem in the theory of conformal mappings. Using a general version of Loewner Theory due to F. Bracci, M.D. Contreras, and S. Díaz-Madrigal [J. Reine Angew. Math. (2012)] we study inhomogeneous branching processes with continuous state and time.

New results presented in the talk are obtained in a joint project with T. Hasebe (Hokkaido University, Sapporo, JAPAN) and J.-L. Pérez Garmendia (Centro de Investigación en Matemáticas, Guanajuato, MÉXICO)

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主讲人4

姓 名

Nikita Gushchin

所在单位

斯科尔科沃科技大学

职称/职务

研究员

简历

Nikita Gushchin于2016至2022年在莫斯科大学获得学士和硕士学位，2022年至今在斯科尔科沃科技大学攻读博士。2023年获得Yandex机器学习奖，2024年获得俄罗斯年轻科学家突破性解决方案国家“AI learders”奖。在机器学习顶级期刊NeurIPS和ICML上以第一作者身份连续发表4篇高质量文章。

报告题目

Building light Schrödinger Bridges

报告

主要观点

The Schrödinger Bridge (SB) problem, originally proposed by Erwin Schrödinger in 1931, seeks the most likely stochastic evolution connecting two probability distributions over time under a reference diffusion process such as Brownian motion. Recently, SBs have attracted growing attention as a promising extension of generative diffusion models, closely related to Entropic Optimal Transport (EOT). Despite notable advances in computational approaches to SBs, most existing solvers remain computationally heavy and require complex optimization of multiple neural networks.

To address this issue, we propose LightSB, a novel lightweight solver for the Schrödinger Bridge problem. LightSB exploits the intrinsic optimal structure of SBs and enables direct minimization of the Kullback–Leibler divergence with respect to the ground-truth solution, using only the start and end marginals.

主讲人照片

主讲人5

姓 名

Makhamat

Gafurov

所在单位

塔什干劳动与社会关系学院

职称/职务

教授

简历

Makhamat Gafurov 1967年在塔什干国立大学获得数学学士学位，随后在俄罗斯科学院斯捷克洛夫数学所和乌兹别克斯坦科学院数学所攻读硕士并于1970年取得硕士学位，1982年在乌兹别克斯坦科学院数学所取得物理和数学博士学位。1989-2024年任塔什干汽车与公路学院数学系教授，2024年至今任塔什干劳动与社会关系学院数学系教授。出版了一部专著和三部教材，发表了70余篇学术论文。目前研究方向为随机游动和离散域的边界问题、随机变量和的极限定理、统计方法与风险分析等。获得了15项优秀科研和教学奖励，为乌兹别克斯坦数学会理事，是包括Bernoulli概率论及数理统计世界大会等多个组织委员会的委员。与波兰、德国、蒙古、中国等国家知名高校进行了卓有成效的学术交流与合作。

报告题目

Boundary Problems for Random Walks in the Theory of Experimental Design

报告

主要观点

This work is devoted to establishing connections between the distributions of certain functionals induced by the exit of a random walk trajectory beyond a curved boundary and stochastic models for calculating the moments of the number of “necessary” experiments required to achieve a prescribed event.

It is established that, with an appropriate choice of a moving boundary and event, the corresponding mathematical models for the mean value and the number of “necessary” experiments can be expressed in terms of infinite series constructed from large deviation probabilities of the Hoeffding–Robbins–Erdös–Katz type, whose convergence is proved by standard methods.

A more interesting part of the work considers the case when the boundary depends on a small parameter. Exact asymptotic behaviors of the series with respect to this small parameter are obtained. It should be emphasized that, in proving this result, it was necessary to refine known results on the asymptotics of series involving large deviation probabilities. In doing so, the author’s own earlier results (1), as well as studies by Chinese colleagues—for example, Y.S. Chow and T.L. Lai (2), Deli Li, Xiangchen Wang, M. Bhaskara (3), Deli Li, Bao-Em Nguyen, and Andrew Rosalsky (4), among others—were employed

主讲人照片

主讲人6

姓 名

Evgeny

Prokopenko

所在单位

索伯列夫研究所（新西伯利亚）

职称/职务

高级研究员

简历

Evgeny Prokopenko2012年在新西伯利亚国立大学获得学士学位，2014年获得硕士学位，2018年在索伯列夫数学所（新西伯利亚）获得数学（概率）博士学位，2019-2021在法国埃塞克高等商学院进行博士后研究工作，现为索伯列夫数学所高级研究员。研究方向为马氏过程、更新过程、极限定理以及随机过程的应用建模和算法等，2022年被华为公司授予技术合作优秀伙伴奖。在Stochastic Processes and their Applications, Statistics and Probability Letters, Markov Processes Relat. Fields等国际知名期刊发表论文20余篇。

报告题目

Stochastic Dynamics Near Critical Points in Stochastic Gradient Descent

报告

主要观点

The talk is devoted to limit theorems for additive stochastic gradient descent (SGD) with a fixed step size that eventually tends to zero. We analyze the local asymptotic behavior of SGD and establish conditions under which the process converges to critical points or remains in their vicinity.

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主讲人7

姓 名

李增沪

所在单位

北京师范大学

职称/职务

教授

简历

李增沪，北京师范大学数学科学院教授，博士生导师，国际数理统计学会会士、国家级人才，曾获高等学校科学研究优秀成果奖自然科学一等奖，作为联合主编获全国优秀教材基础教育类特等奖，曾任中国数学会概率统计分会主任，现任中国数学会数学教育工作委员会副主任。在概率论顶级期刊The Annals of Probability, Probability Theory and Related Fields,The Annals of Applied Probability等上发表研究论文 80 多篇，出版研究专著 1 部 (Springer 2011)。英文专著被美国《数学评论》认为是测度值分枝过程领域第一部教科书式的专著 (the first monograph in textbook format)，提供了有力而广泛的 (powerful and general) 方法，引进的“斜卷积半群”概念被认为对带移民分枝过程的研究扮演了关键角色 (key role)。与合作者建立的分枝马氏过程的随机方程在文献中被称为“Dawson-Li 方程”或“Dawson-Li 表示”，被认为是强/有力的工具 (strong tool, powerful tools)，已被应用于复杂群体演化、随机能量模型、金融与经济模型等的研究，知名学者在专著 (Springer 2016) 中用整章篇幅讨论。

报告题目

Stochastic integral representations for the Lévy forest

报告

主要观点

A stochastic integral representation is proved for the local time of the height process of a spectrally positive Lévy process stopped at a hitting time. From the representation we derive a strong stochastic equation of the type of Dawson and Li (Ann. Probab., 2012). This leads to a representation of the Ray-Knight theorem of Le Gall and Le Jan (Ann. Probab., 1998) and Duquesne and Le Gall (Astérisque, 2002), which codes the genealogical forest of a continuous-state branching process. The result extends the recent work of Aidékon et al. (Sci. China Math., 2024) for a Brownian motion with a local time drift.

主讲人照片

主讲人8

姓 名

任艳霞

所在单位

北京大学

职称/职务

教授

简历

任艳霞，北京大学数学科学学院教授、博士生导师，北京大学统计科学中心教授，概率统计系主任。1982年进入河北大学数学系学习，先后获理学学士和硕士学位，1998年获南开大学数学学院博士学位。中国概率统计学会第九届、第十届常务理事。 1989年起任河北科技大学讲师、副教授，1998年进入清华大学高等研究中心从事博士后研究。2000年调入北京大学数学科学学院任副教授，2003年晋升教授。长期从事测度值马氏过程、交互粒子系统、概率位势理论和非线性偏微分方程研究，主持8项国家自然科学基金项目及多项博士后基金、高等学校博士点基金项目。2000年获全国优秀博士论文奖，2009年参与项目获国家级教学成果二等奖。主讲应用随机过程等课程，2024年获北京大学曾宪梓优秀教学奖。在概率顶级期刊The Annals of Probability, Bernoulli, Stochastic Processes and Their Applications, Annales de l’Institut Henri Poincaré等国际学术期刊上发表研究论文90多篇。

报告题目

Moments of additive martingales of branching Levy processes and some applications

报告

主要观点

Let Wt(θ) be the Biggins martingale of a supercritical branching Lévy process with non-local branching mechanism, and denote by W∞(θ) its limit. In this talk, we first study properties of W∞(θ). We provide sufficient and necessary conditions for W∞(θ) to have finite pth moment and sufficient conditions for E(W∞(θ) pL(W∞(θ)) < ∞, where L is slowly varying at infinity. We also study the tail behavior of W∞(θ). We then use our results on W∞(θ) to establish central limit theorems and stable central limit theorems for Wt(θ) − W∞(θ) . The talk is based on joint work with Renming Song and Rui Zhang.

主讲人照片

主讲人9

姓 名

石权

所在单位

中科院数学与系统科学研究院

职称/职务

副教授

简历

石权，中科院数学与系统科学研究院副教授，本科毕业于清华大学，2013-2016年在瑞士苏黎世大学攻读数学博士学位，法国巴黎十三大博士后, 2017-2019年英国牛津大学访问研究员，2019-2021年德国曼海姆大学研究助理，2021年至今，中国科学院数学与系统科学研究院副研究员。研究方向为增长分裂过程、随机树、列维过程和分枝粒子系统，在概率著名期刊The Annals of Applied Probability, Bernoulli, Electronic Journal of Probability, Annales de l’Institut Henri Poincaré (Probabilités et Statistiques), Stochastic Processes and Their Applications等发表研究论文10余篇。

报告题目

Stochastic Flows and Interval-Partition Evolutions

报告

主要观点

The Ray-Knight theorems establish a fundamental connection between Brownian local time and squared Bessel processes. Recently, Aïdékon–Hu–Shi extended this framework to an infinite-dimensional representation via stochastic flows, inheriting the spirit of the works of Bertoin–Le Gall and Dawson–Li. Building on their framework, we study a pair of coupled stochastic squared Bessel flows parametrised by $\delta\in (0,2)$ and construct a partition of the space-time plane $\mathbb{R}_+\times \mathbb{R}$. We prove that these partitions correspond to squared Bessel excursions with a negative parameter $-\delta$, which are naturally embedded within the jumps of a spectrally positive $(1+\delta/2)$ stable process.  This connection further allows us to relate these structures to Björnberg–Curien–Stefánsson's shredded sphere, and to interval-partition evolutions introduced in a series of works by Forman–Pal–Rizzolo–Winkel. 
Joint work with Elie Aïdékon (Fudan University) and Chengshi Wang (Fudan University). 

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主讲人10

姓 名

向开南

所在单位

湘潭大学

职称/职务

教授

简历

向开南，湘潭大学数学与计算科学学院教授，博士生导师，1993年获湘潭大学数学系学士学位，1996年、1999年先后在北京师范大学、中国科学院应用数学研究所取得硕士及博士学位，1999年至2001年在北京大学从事博士后研究。2001年入职湖南师范大学，2007-2019年任南开大学数学科学学院教授，2019年至今任湘潭大学工作。2005年入选教育部新世纪优秀人才支持计划。研究方向涵盖概率论、随机过程及其与图论组合、统计物理的交叉领域。2010年在《Comm. Pure Appl. Math.》独立发表解决超布朗运动的Schilder型定理猜想；2023年与合作在《Comm. Pure Appl. Math.》发表攻克非初等双曲群上分枝随机游走临界指数普适性的猜想。获钟家庆优秀论文奖。在国际著名期刊, Trans. Amer. Math. Soc., Ann. Probab.，Bernoulli, Ann. Inst. Henri Poincaré Probab. Stat., Bernoulli等发表研究论文60多篇。

报告题目

The probabilistic approach to the Jacobian conjecture

报告

主要观点

In this talk, we will describe and discuss the following probabilistic approach to the Jacobian conjecture, introduced by E. Bisi, P. Dyszewski, N. Gantert, S. G. G. Johnston, J. Prochno and D. Schmid [ (2023). Random planar trees and the Jacobian conjecture. arXiv:2301.08221v3 [math.CO], Preprint.]: If there is an integer d such that for all natural numbers p, there exists a p-shuffle Markov chain on large d-Catalan trees with the uniform distribution being its stationary distribution, then the Jacobian conjecture is true. And we will also discuss our own related probability questions. The Jacobian conjecture, proposed by Ott-Heinrich Keller in 1939, says that any polynomial mapping on Cn with a nonzero constant Jacobian determinant has an inverse polynomial mapping. As one of the outstanding open problems in all of mathematics (particularly in algebraic geometry), the conjecture was listed as one of 18 mathematical problems for the 21st century by Steve Smale in 1998.

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主讲人11

姓 名

严晓东

所在单位

西安交通大学

职称/职务

教授

简历

严晓东，西安交通大学数学与统计学院教授，博士生导师，入选国家级青年人才项目和校内青拔A类支持计划，荣获“华为火花奖”，“滴滴盖亚学者”, 研究方为统计决策、统计推断和统计计算等。学术成果发表在著名期刊JRSSB, AOS, JASA, JOE 以及人工智能顶级会议 NeurIPS,ICMI,AAAI等 50余篇。 在“高等教育出版社出版”以独立主编出版了《机器学习》、《数据科学实践基础-基于R》两部教材。

报告题目

AI for Probability：A Task-driven Limit Theory and Some Statistical Application

报告

主要观点

The development of AI models can be divided into three stages: traditional statistical learning, machine/deep learning, and today’s task-driven large-model era. In each stage, probability-based uncertainty quantification has its own meaning and methodology. Task-driven statistical methods differ fundamentally from traditional data- or model-driven approaches: task-driven AI acts as a task engine, built on information engines formed by data- and model-driven methods. Better information engines support better decisions for specific goals. Yet a complete limit theory for uncertainty quantification in this “task-driven probability” framework is still missing.

This talk builds on multi-armed bandit models. By breaking the classical exchangeability assumption and mapping uncertainty distributions into a strategy space, we study the law of large numbers and central limit theorem in a broader distributional setting, leading to a strategic law of large numbers and a strategic central limit theorem. Probabilistically, this extends nonlinear expectation theory to data-level statistical applications, and reveals several paradoxes such as “independent + independent = dependent,” “good + bad = better,” and “normal + normal = non-normal,” highlighting the limits of traditional data-driven methods for task-driven goals. Statistically, we show how strategic limit theory applies to estimation and hypothesis testing, explain its mathematical logic and advantages, and illustrate the unique strengths of a task-driven statistical mindset through business cases from DiDi and Huawei.

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主讲人12

姓 名

廖仲威

所在单位

北京师范大学（珠海）

职称/职务

副教授

简历

廖仲威，北京师范大学文理学院数学系（珠海）副教授，博士生导师。毕业于北京师范大学，曾在中山大学、华南师范大学任教，并在澳大利亚墨尔本大学、加拿大多伦多都会大学担任博士后及访问学者。研究方向包括随机过程稳定性、Lévy过程、金融数学等，,主持国家自然科学基金、广东省基础与应用基础基金等项目, 在国际知名期刊SIAM J. Control Optim., J. Theoret. Probab., J. Appl. Probab.等发表研究论文十多篇。

报告题目

Inferring and forecasting the volatility of cryptocurrency under regime-switching distributed-delay stochastic model

报告

主要观点

We propose a regime-switching volatility model for cryptocurrency that mathematically couples a classical Ornstein-Uhlenbeck (OU) process with a distributed-delay OU (delay-OU) process. This structure allows volatility to alternate between regimes of fast mean reversion and memory-dependent mean reversion. Methodologically, we extend the Expectation-Maximization (EM) framework to accommodate delayed mean-reverting emissions and design a regime-aware forecasting scheme. This scheme combines regime-conditional predictions with inferred regime state probabilities. Empirically, using daily log-realized variance constructed from high-frequency prices, the model achieves strong in-sample fit and reveals an interpretable latent regime path: a low-volatility, persistent delay-OU regime and a high-volatility OU regime. Transitions between these regimes align with salient macroeconomic and financial events. Out of sample, the regime-switching forecaster consistently outperforms single-regime OU and delay-OU benchmarks. This synthesis of regime heterogeneity and delayed mean reversion improves volatility inference and prediction in cryptocurrency markets and furnishes quantitative diagnostics of macro-financial regime transitions.

主讲人照片