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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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Entropic Dynamics of Jump-Diffusion Option Pricing [PDF]
EntropyThe standard models of stock-price dynamics and option valuation rest on stochastic processes postulated at the outset; here, we lay down an entropic-inference framework that derives these processes rather than assuming them, by making explicit the ...
Mohammad Abedi
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Frontiers in PhysicsThe stock price data are sampled at discrete times (e.g., hourly, daily, weekly, etc). When data are sampled at discrete times, they appear as a sequence of discontinuous jump events, even if they have been sampled from a continuous process. On the other
Ali Asghar Movahed, Houshyar Noshad
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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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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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