scholarly journals Likelihood theory for the graph Ornstein-Uhlenbeck process

2021 ◽  
Author(s):  
Valentin Courgeau ◽  
Almut E. D. Veraart
Keyword(s):  
Lévy Process ◽  
Network Effects ◽  
Asymptotic Theory ◽  
Maximum Likelihood Estimators ◽  
Levy Process ◽  
Adaptive Lasso ◽  
Graph Structure ◽  
Uhlenbeck Process ◽  
Penalised Likelihood ◽  
The Impact

AbstractWe consider the problem of modelling restricted interactions between continuously-observed time series as given by a known static graph (or network) structure. For this purpose, we define a parametric multivariate Graph Ornstein-Uhlenbeck (GrOU) process driven by a general Lévy process to study the momentum and network effects amongst nodes, effects that quantify the impact of a node on itself and that of its neighbours, respectively. We derive the maximum likelihood estimators (MLEs) and their usual properties (existence, uniqueness and efficiency) along with their asymptotic normality and consistency. Additionally, an Adaptive Lasso approach, or a penalised likelihood scheme, infers both the graph structure along with the GrOU parameters concurrently and is shown to satisfy similar properties. Finally, we show that the asymptotic theory extends to the case when stochastic volatility modulation of the driving Lévy process is considered.

scholarly journals Stochastic differential of Ito – Levy processes

2016 ◽  
Vol 19 (2) ◽  
pp. 80-83
Author(s):  
Dam Ton Duong ◽  
Phung Ngoc Nguyen
Keyword(s):  
Information Technology ◽  
Stochastic Processes ◽  
Lévy Process ◽  
Jump Process ◽  
Levy Processes ◽  
Levy Process ◽  
Product Rule ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Geometric Levy Process

In this paper, we continue to expand some results to get the product rule for differential of stochastic processes with jump, and apply for some special processes like pure jump process, Levy-Ornstein-Uhlenbeck process, geometric Levy process, in models of finance, ecomomics, and information technology.

Transformation of education as a metatrend of the digital economy

2020 ◽  
Vol 16 (10) ◽  
pp. 1960-1979
Author(s):  
N.A. Egina ◽  
E.S. Zemskova
Keyword(s):  
Human Capital ◽  
Social Transformation ◽  
Network Effects ◽  
Digital Economy ◽  
Network Education ◽  
Economic Progress ◽  
Positive Externalities ◽  
Communication Processes ◽  
Education Network ◽  
The Impact

Subject. The study focuses on the impact of the digital economy determinants of the education transformation. Objectives. The article provides our own approach treating the education capital as a specific asset of the digital economy, which has an acceleration effect and sets up new trends in education through integrative networks. Methods. The study is based on principles of the systems integration, cross-disciplinary and multidisciplinary approaches. Results. The socio-economic progress was found to be determined with properties of human capital, which are solely specific to the digital economy. In new circumstances, it gets more important for actors of global, national, corporate and social networks to more actively cooperate within distributed networks in order to train high professionals, who would have skills in information networks. Thus, they would raise a new form of human capital – the capital of network education (network-based education capital). We describe positive externalities that arise when the educational sector joins communication processes. We illustrate how educational forms evolves, which are typical of a certain phase of the socio-economic development. The education capital was discovered to grow into a specific asset generating the quasi-rent and working as a social ladder only provided more actors are involved into the network. Conclusions and Relevance. Studying the evolution of educational forms through the cross-disciplinary method, we discovered the need for a system approach, which would help substantiate its transformation in the time of the digital economy, and the emergence of network-based education. These are technologies and tools of the digital economy that become unique factors generating the acceleration effect of the educational capital and ensuring the use of diverse network effects for the formation of intellectual capital and their social transformation.

Principles for sharing economy formation in the digital society

2020 ◽  
Vol 16 (5) ◽  
pp. 800-821
Author(s):  
E.V. Popov ◽  
K.A. Semyachkov
Keyword(s):  
Network Effects ◽  
Sharing Economy ◽  
Network Effect ◽  
Industrial Society ◽  
Economic Activities ◽  
Digital Platforms ◽  
Digital Society ◽  
Modern Economy ◽  
Characteristic Features ◽  
The Impact

Subject. The article addresses economic relations that are formed in various areas of economic application of digital platforms. The target of the research is the modern economy of digital platforms across different economic activities. Objectives. The aim is to systematize principles for share economy formation in the context of the digital society development. Methods. We employ general scientific methods of research. Results. The study shows that the development of digital platforms is one of the most important trends in the development of the modern economy. We classified certain characteristic features of modern digital platforms, analyzed principles for their creation. The paper emphasizes that the network effects achieved through the use of digital platforms are an important factor in the development of the share economy. The network effect describes the impact of the number of the platform users on the value created for each of them. The paper also considers differences in the organization of traditional economy companies and companies that are based on the digital platform model, reveals specifics of changes in socio-economic systems caused by the development of digital platforms, systematizes principles of the sharing economy formation in the context of the digital society development. Conclusions. The analyzed principles for sharing economy development on the basis of digital platforms can be applied to create models for the purpose of forecasting the transformation of economic activity in the post-industrial society.

scholarly journals LAN property for a simple Lévy process

2014 ◽  
Vol 352 (10) ◽  
pp. 859-864 ◽  
Author(s):  
Arturo Kohatsu-Higa ◽  
Eulalia Nualart ◽  
Ngoc Khue Tran
Keyword(s):  
Lévy Process ◽  
Levy Process

scholarly journals On the optimal dividend problem for a spectrally negative Lévy process

2007 ◽  
Vol 17 (1) ◽  
pp. 156-180 ◽  
Author(s):  
Florin Avram ◽  
Zbigniew Palmowski ◽  
Martijn R. Pistorius
Keyword(s):  
Lévy Process ◽  
Levy Process ◽  
Spectrally Negative Lévy Process ◽  
Optimal Dividend
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