Jump Processes and Special Problems

1998 ◽  
pp. 147-182
Author(s):  
Charles S. Tapiero
Keyword(s):  
Jump Processes

High-Frequency Financial Econometrics

2014 ◽  
Author(s):  
Yacine Aït-Sahalia ◽  
Jean Jacod
Keyword(s):  
High Frequency ◽  
Practical Importance ◽  
Financial Econometrics ◽  
Trading Strategies ◽  
Financial Data ◽  
Jump Processes ◽  
High Frequency Trading ◽  
Microstructure Noise ◽  
Econometric Methods ◽  
Mathematical Foundations

High-frequency trading is an algorithm-based computerized trading practice that allows firms to trade stocks in milliseconds. Over the last fifteen years, the use of statistical and econometric methods for analyzing high-frequency financial data has grown exponentially. This growth has been driven by the increasing availability of such data, the technological advancements that make high-frequency trading strategies possible, and the need of practitioners to analyze these data. This comprehensive book introduces readers to these emerging methods and tools of analysis. The book covers the mathematical foundations of stochastic processes, describes the primary characteristics of high-frequency financial data, and presents the asymptotic concepts that their analysis relies on. It also deals with estimation of the volatility portion of the model, including methods that are robust to market microstructure noise, and address estimation and testing questions involving the jump part of the model. As the book demonstrates, the practical importance and relevance of jumps in financial data are universally recognized, but only recently have econometric methods become available to rigorously analyze jump processes. The book approaches high-frequency econometrics with a distinct focus on the financial side of matters while maintaining technical rigor, which makes this book invaluable to researchers and practitioners alike.

Filtering of Jump Processes.

1987 ◽  
Author(s):  
Robert J. Elliott
Keyword(s):  
Jump Processes

scholarly journals Exact statistical solution for the hopping transport of trapped charge via finite Markov jump processes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Andrey A. Pil’nik ◽  
Andrey A. Chernov ◽  
Damir R. Islamov
Keyword(s):  
Charge Transport ◽  
Thin Layers ◽  
Jump Processes ◽  
Dielectric Films ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Statistical Solution ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
Thin Dielectric Films

AbstractIn this study, we developed a discrete theory of the charge transport in thin dielectric films by trapped electrons or holes, that is applicable both for the case of countable and a large number of traps. It was shown that Shockley–Read–Hall-like transport equations, which describe the 1D transport through dielectric layers, might incorrectly describe the charge flow through ultra-thin layers with a countable number of traps, taking into account the injection from and extraction to electrodes (contacts). A comparison with other theoretical models shows a good agreement. The developed model can be applied to one-, two- and three-dimensional systems. The model, formulated in a system of linear algebraic equations, can be implemented in the computational code using different optimized libraries. We demonstrated that analytical solutions can be found for stationary cases for any trap distribution and for the dynamics of system evolution for special cases. These solutions can be used to test the code and for studying the charge transport properties of thin dielectric films.

scholarly journals Fast Reaction Limits via $$\Gamma $$-Convergence of the Flux Rate Functional

2021 ◽  
Author(s):  
Mark A. Peletier ◽  
D. R. Michiel Renger
Keyword(s):  
Evolution Equations ◽  
Detailed Balance ◽  
Approximate Solutions ◽  
Reaction Rates ◽  
Convergence Result ◽  
Rate Function ◽  
Jump Processes ◽  
Kolmogorov Equations ◽  
Markov Jump ◽  
Fast Reaction

AbstractWe study the convergence of a sequence of evolution equations for measures supported on the nodes of a graph. The evolution equations themselves can be interpreted as the forward Kolmogorov equations of Markov jump processes, or equivalently as the equations for the concentrations in a network of linear reactions. The jump rates or reaction rates are divided in two classes; ‘slow’ rates are constant, and ‘fast’ rates are scaled as $$1/\epsilon $$ 1 / ϵ , and we prove the convergence in the fast-reaction limit $$\epsilon \rightarrow 0$$ ϵ → 0 . We establish a $$\Gamma $$ Γ -convergence result for the rate functional in terms of both the concentration at each node and the flux over each edge (the level-2.5 rate function). The limiting system is again described by a functional, and characterises both fast and slow fluxes in the system. This method of proof has three advantages. First, no condition of detailed balance is required. Secondly, the formulation in terms of concentration and flux leads to a short and simple proof of the $$\Gamma $$ Γ -convergence; the price to pay is a more involved compactness proof. Finally, the method of proof deals with approximate solutions, for which the functional is not zero but small, without any changes.

scholarly journals Research on the Sustainable Operation of Low-Carbon Tourism Supply Chain under Sudden Crisis Prediction

2021 ◽  
Vol 13 (15) ◽  
pp. 8228
Author(s):  
Lu Zhang ◽  
Deqing Ma ◽  
Jinsong Hu
Keyword(s):  
Supply Chain ◽  
Jump Processes ◽  
Travel Agency ◽  
Tourist Attraction ◽  
Low Carbon ◽  
Sustainable Operations ◽  
The Sustainable Development ◽  
Crisis Events ◽  
Continuous Dynamic ◽  
Tourism Supply Chain

This paper integrates a low-carbon tourism supply chain consisting of a low-carbon tourist attraction (LTA) providing a low-carbon service and an online travel agency (OTA) responsible for big data marketing. Consumers may also encounter sudden crisis events that occur in the tourist attraction during their visit, and the occurrence of crisis events can damage the low-carbon goodwill of the tourist attraction to the detriment of the sustainable development of the supply chain. Therefore, this paper aims to investigate how tourism firms can develop dynamic strategies in the pre-crisis environment if they envision the occurrence of a crisis event and how crisis events affect interfirm cooperation. This paper uses stochastic jump processes to portray the dynamic evolution of low-carbon goodwill in the context of crisis events and introduces the methods of the differential game and Bellman’s continuous dynamic programming theory to study the sustainable operations of low-carbon tourism supply chains. Our findings provide important managerial insights for enterprises in the tourism supply chain and suggest that they need to not only become aware of the tourist attraction crisis events, but also, more importantly, they need to adjust their appropriate input strategies based on the degree of anticipation of the crisis.

Jump processes and nonlinear fractional heat equations on metric measure spaces

2006 ◽  
Vol 279 (1-2) ◽  
pp. 150-163 ◽  
Author(s):  
Jiaxin Hu ◽  
Martina Zähle
Keyword(s):  
Jump Processes ◽  
Heat Equations ◽  
Metric Measure Spaces ◽  
Measure Spaces
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