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Modular Jump Gaussian Processes
Data Science in ScienceGaussian processes (GPs) furnish accurate nonlinear predictions with well-calibrated uncertainty. However, the typical GP setup has a built-in stationarity assumption, making it ill-suited for modeling data from processes with sudden changes, or “jumps ...
Anna R. Flowers +4 more
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On Itô formulas for jump processes [PDF]
Queueing Systems, 2021 AbstractA well-known Itô formula for finite-dimensional processes, given in terms of stochastic integrals with respect to Wiener processes and Poisson random measures, is revisited and is revised. The revised formula, which corresponds to the classical Itô formula for semimartingales with jumps, is then used to obtain a generalisation of an important ...
István Gyöngy, Sizhou Wu
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Entropy, 2021 A family of heterogeneous mean-field systems with jumps is analyzed. These systems are constructed as a Gibbs measure on block graphs. When the total number of particles goes to infinity, the law of large numbers is shown to hold in a multi-class context,
Donald A. Dawson +2 more
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A modified Φ-Sobolev inequality for canonical Lévy processes and its applications
Modern Stochastics: Theory and Applications, 2023 A new modified Φ-Sobolev inequality for canonical ${L^{2}}$-Lévy processes, which are hybrid cases of the Brownian motion and pure jump-Lévy processes, is developed.
Noriyoshi Sakuma, Ryoichi Suzuki
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Estimating Equations for Density Dependent Markov Jump Processes
Mathematics, 2021 Reaction networks are important tools for modeling a variety of biological phenomena across a wide range of scales, for example as models of gene regulation within a cell or infectious disease outbreaks in a population. Hence, calibrating these models to
Oluseyi Odubote, Daniel F. Linder
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Regularity of models associated with Markov jump processes
Open Mathematics, 2022 We consider a jump Markov process X=(Xt)t≥0X={\left({X}_{t})}_{t\ge 0}, with values in a state space (E,ℰ)\left(E,{\mathcal{ {\mathcal E} }}). We suppose that the corresponding infinitesimal generator πθ(x,dy),x∈E{\pi }_{\theta }\left(x,{\rm{d}}y),x\in E,
Jedidi Wissem
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Modeling Regulation of Economic Sustainability in Energy Systems with Diversified Resources
Sci, 2021 The imperfection of theoretical and methodological approaches to regulate the jump process transition when combining differentiated energy resources is a pressing issue.
Anatoly Alabugin, Sergei Aliukov
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Game-Theoretic Optimal Portfolios for Jump Diffusions
Games, 2019 This paper studies a two-person trading game in continuous time that generalizes Garivaltis (2018) to allow for stock prices that both jump and diffuse.
Alex Garivaltis
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Interest-Rate Products Pricing Problems with Uncertain Jump Processes
Discrete Dynamics in Nature and Society, 2021 Uncertain differential equations (UDEs) with jumps are an essential tool to model the dynamic uncertain systems with dramatic changes. The interest rates, impacted heavily by human uncertainty, are assumed to follow UDEs with jumps in ideal markets ...
Yiyao Sun, Shiqin Liu
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Symmetric Jump Processes [PDF]
Transactions of the American Mathematical Society, 1974 We use the theory of Dirichlet spaces to construct symmetric Markov processes of pure jump type and to identify the Lévy measures for these processes. Particular attention is paid to lattice and hard sphere systems which interact through speed change and exclusion.
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