Кельберт Марк Яковлевич
Факультет экономических наук
Профессиональные интересы
Должности
- Профессор-исследователь — Факультет экономических наук, Департамент статистики и анализа данных
- Ведущий научный сотрудник — Факультет экономических наук, Международная лаборатория стохастического анализа и его приложений
Био
- · Начал работать в НИУ ВШЭ в 2014 году.
- · Научно-педагогический стаж: 73 года.
Образование
- 1982 · Кандидат физико-математических наук
- 1968 · Специалитет: Московский государственный университет им. М.В. Ломоносова, факультет: мех-мат, специальность «Математика», квалификация «Математик»
Опыт работы
- · 1993-1998: Lecturer at European Business School, Swansea University, UK
- · 1998-2004: Reader at European Business School, Swansea University, UK
- · 2004-2014: Reader at Department of Mathematics, Swansea University, UK
- · 2014: Начал работать в НИУ ВШЭ в году
- · Научно-педагогический стаж: 49 лет.
Награды и поощрения
- · Почетная грамота НИУ ВШЭ (декабрь 2025)
- · Медаль "Признание - 10 лет успешной работы" НИУ ВШЭ (ноябрь 2025)
- · Благодарность департамента статистики и анализа данных НИУ ВШЭ (январь 2025)
- · Благодарность факультета экономических наук НИУ ВШЭ (январь 2022)
- · Благодарность проректора НИУ ВШЭ (август 2021)
- · Благодарственное письмо ректора НИУ ВШЭ (ноябрь 2020)
- · Надбавка за публикацию в международном рецензируемом научном издании (2022–2023, 2021–2022, 2020–2022, 2017–2019)
- · Надбавка за регулярные публикации в международных рецензируемых научных изданиях (2024–2029, 2023–2028)
- · Надбавка за статью в зарубежном рецензируемом журнале (2015–2017)
- · Победитель Конкурса лучших русскоязычных научных и научно-популярных работ работников НИУ ВШЭ – 2022
Гранты и проекты
- — · Я был научным руководителем нескольких грантов в Великобритании: EPSRC, British Academy,
- — · London Mathematical Society и т. д. Кроме того. я получал гранты в Бразилии (FAPESP).
Конференции (2)
Показать все
- · 39-я междисциплинарная школа-конференция "Информационные технологии и системы 2015", ИППИ РАН, Сочи, Сентябрь 2015.
- · "Asymptotic analysis of the Renyi, Tsallis and Fisher entropies in a Bayesian problem"
Идентификаторы исследователя
- ORCID:
0000-0002-3952-2012 - ResearcherID:
F-7255-2016 - SPIN РИНЦ:
7972-7182 - Google Scholar: https://scholar.google.com/citations?user=Okrgp24AAAAJ&hl=en
- Scopus AuthorID:
55884702600
Публикации (53)
Survey on Scale Functions for Spectrally Negative Lévy Processes
2018 · ARTICLE · en
This article gives a brief summary on the main theoretical and practical results for the Scale functions. The article is organized in the following way: the first part describes the main theoretical concepts of Lévy processes, gives the formal definition and analytical properties of the Scale function. The second part describes the most significant practical cases where the Scale functions are applied. Thereafter, the closed-form expressions of Scale functions for several classes of spectrally negative Lévy processes are considered. Finally, we concentrate on the very important application of Scale functions, namely, derivation of the distribution of dividends, paid by the insurance company to shareholders. The main contribution of this article is a lemma, describing the asymptotic behaviour of dividends, paid by nidentical companies
Generalization of Cram´er-Rao and Bhattacharyya inequalities for the weighted covariance matrix
2017 · ARTICLE · en
The paper considers a family of probability distributions depending on a pa- rameter. The goal is to derive the generalized versions of Cram´er-Rao and Bhattacharyya inequalities for the weighted covariance matrix and of the Kullback inequality for the weighted Kullback distance, which are important objects themselves [9, 23, 28]. The asymp- totic forms of these inequalities for a particular family of probability distributions and for a particular class of continuous weight functions are given.
Asymptotic behaviour of non-isotropic random walks with heavy tails
2017 · ARTICLE · en
A random flight on a plane with non-isotropic displacements at the moments of direction changes is considered. In the case of exponentially distributed flight lengths a Gaussian limit theorem is proved for the position of a particle in the scheme of series when jump lengths and non-isotropic displacements tend to zero. If the flight lengths have a folded Cauchy distribution the limiting distribution of the particle position is a convolution of the circular bivariate Cauchy distribution with a Gaussian law.
Weighted entropy: basic inequalities
2017 · ARTICLE · en
This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy contextdependent, through the weight function. We analyse analogs of the Fisher information inequality and entropy power inequality for the weighted entropy and discuss connections with weighted Lieb’s splitting inequality. The concepts of rates of the weighted entropy and information are also discussed.
Modelling Stochastic and Deterministic Behaviours in Virus Infection Dynamics
2017 · ARTICLE · en
Many human infections with viruses such as human immunode ciency virus type 1 (HIV{1) are characterized by low numbers of founder viruses for which the random effects and discrete nature of populations have a strong effect on the dynamics, e.g., extinction versus spread. It remains to be established whether HIV transmission is a stochastic process on the whole. In this study, we consider the simplest (so-called, 'consensus') virus dynamics model and develop a computational methodology for building an equivalent stochastic model based on Markov Chain accounting for random interactions between the components. The model is used to study the evolution of the probability densities for the virus and target cell populations. It predicts the probability of infection spread as a function of the number of the transmitted viruses. A hybrid algorithm is suggested to compute efficiently the dynamics in state space domain characterized by a mix of small and large species densities.
Weighted Entropy and its Use in Computer Science and Beyond
2017 · CHAPTER · en
The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of the Fisher information inequality and entropy-power inequality for the weighted entropy and discuss connections with weighted Lieb’s splitting inequality. The concepts of rates of the weighted entropy and information are also discussed.
Information Theory and Coding
2017 · BOOK · zh
Эта книга включает стандартный пакет информационно-теоретического материала, обычно читаемого на факультетахинформатики и электроники, а также прикладной математики, ведущих университетов, наряду с некоторыми новыми результатами. При этом излагаются как вероятнростные, так и алгебраические аспекты теории информации и кодирования, включая как основы теории, так и некоторые ее современные аспекты. Предмет этой книги критически важен для современных приложений ( телекоммуникации, обработка сигналов, информатика, криптография).
Basic inequalities for weighted entropies
2016 · ARTICLE · en
The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We establish a number of besic inequalities mirroring similar bounds on standard shannon entropy and related quantities
Random migration processes between two stochastic epidemic centers
2016 · ARTICLE · en
We consider the epidemic dynamics in stochastically interacting population centers coupled by a random migration.
Weak error for Continuous Time Markov Chains related to fractional in time P(I)DEs
2016 · ARTICLE · en
We provide sharp error bounds for the difference between the transition densities of some multidimensional Continuous Time Markov Chains (CTMC) and the fundamental solutions of some fractional in time Partial (Integro) Differential Equations (P(I)DEs). Namely, we consider equations involving a time fractional derivative of Caputo type and a spatial operator corresponding to the generator of a non degenerate Brownian or stable driven Stochastic Differential Equation (SDE).
Курсы (1)
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Методологический научно-исследовательский семинар
2023/2024 · Магистратура · рус