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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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Boundary Harnack inequality for Markov processes with jumps [PDF]
, 2013 We prove a boundary Harnack inequality for jump-type Markov processes on metric measure state spaces, under comparability estimates of the jump kernel and Urysohn-type property of the domain of the generator of the process.
Bogdan, Krzysztof +2 more
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Jump Variation Estimation with Noisy High Frequency Financial Data via Wavelets
Econometrics, 2016 This paper develops a method to improve the estimation of jump variation using high frequency data with the existence of market microstructure noises. Accurate estimation of jump variation is in high demand, as it is an important component of volatility ...
Xin Zhang, Donggyu Kim, Yazhen Wang
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Journal of Statistical Software, 2023 We introduce a Python library, called jumpdiff, which includes all necessary functions to assess jump-diffusion processes. This library includes functions which compute a set of non-parametric estimators of all contributions composing a jump-diffusion ...
Leonardo Rydin Gorjão +2 more
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On the consistency of jump-diffusion dynamics for FX rates under inversion [PDF]
, 2019 In this note we investigate the consistency under inversion of jump diffusion processes in the Foreign Exchange (FX) market. In other terms, if the EUR/USD FX rate follows a given type of dynamics, under which conditions will USD/EUR follow the same type
Brigo, Damiano +2 more
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Option Pricing with Stochastic Volatility and Jump Diffusion Processes [PDF]
Theoretical and Applied Economics, 2006 Option pricing by the use of Black Scholes Merton (BSM) model is based on the assumption that asset prices have a lognormal distribution. In spite of the use of these models on a large scale, both by practioners and academics, the assumption of ...
Radu Lupu
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Probabilistic Resistive Switching Device Modeling Based on Markov Jump Processes
IEEE Access, 2021 In this work, a versatile mathematical framework for multi-state probabilistic modeling of Resistive Switching (RS) devices is proposed for the first time. The mathematical formulation of memristor and Markov jump processes are combined and, by using the
Vasileios Ntinas +2 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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, 2022 A jump process is a type of stochastic process that has discrete movements, called jumps, with random arrival times, rather than continuous movement, typically modelled as a simple or compound Poisson process.
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