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Rates of convergence to the local time of Oscillating and Skew Brownian Motions
TLDR
In this article, a class of statistics based on high frequency observations of oscillating Brownian motions and skew Brownian motion is considered and their convergence rate towards the local time of the underling process is obtained in form of a Central Limit Theorem.Abstract:
In this paper a class of statistics based on high frequency observations of oscillating Brownian motions and skew Brownian motions is considered. Their convergence rate towards the local time of the underling process is obtained in form of a Central Limit Theorem.read more
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Filling the gaps
TL;DR: McFedries as mentioned in this paper examines new words and phrases that have jumped down from their technological niches and are poised to set up shop in the broader piazza of general language use.
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Drift estimation of the threshold Ornstein-Uhlenbeck process from continuous and discrete observations
Sara Mazzonetto,Paolo Pigato +1 more
TL;DR: In this paper, the authors refer by threshold Ornstein-Uhlenbeck to a continuous-time threshold autoregressive process and develop a test for the presence of a threshold in the dynamics.
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Data and methods for A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data [Données et méthodes pour "A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data"]
Antoine Lejay,Paolo Pigato +1 more
TL;DR: In this paper, the authors presented the methodology and numerical results for 21 stock prices under the assumption they follow a Drifted Geometric Oscillating Brownian motion model, taking leverage and mean-reversion effects into account.
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Functional convergence to the local time of a sticky diffusion
TL;DR: In this paper , the convergence of a class of high frequency path-functionals of a sticky diffusion to its local time is proved. And the authors extend the result to sticky stochastic differential equations and combine the local time approximation with an approximation of the occupation time.
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Bi-Directional Grid Constrained Stochastic Processes' Link to Multi-Skew Brownian Motion
TL;DR: In this paper, the authors identify that BGCSPs are a variant rather than a special case of the multi-skew Brownian motion (M-SBM), and provide an M-sBM theoretical framework and also a simulation framework to elaborate deeper properties of BGCSTP.
References
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Stopping Times and Tightness. II
TL;DR: In this article, it was shown that weak convergence to a continuous limit process can be deduced almost immediately from convergence of finite-dimensional distributions, under a technical tightness condition involving stopping times and predictability of imminent jumps.
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On Mixing and Stability of Limit Theorems
David Aldous,G. K. Eagleson +1 more
TL;DR: In this article, the central limit theorem for martingales can be obtained directly using stability, and the proofs seem substantially simpler than those previously given. But they are not new results.
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On Skew Brownian Motion
J. M Harrison,Larry Shepp +1 more
TL;DR: In this article, the authors considered the stochastic equation where W(t) is a standard Wiener process and L^X_0 (cdot) is the local time at zero of the unknown process.
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On estimating the diffusion coefficient from discrete observations
TL;DR: In this paper, an estimator of σ based on discrete observation of the diffusion X throughout a given finite time interval is proposed and the asymptotic behavior of this estimator when the step of discretization tends to zero.
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On the constructions of the skew Brownian motion
TL;DR: The authors summarizes the various ways one may use to construct the Skew Brownian motion, and shows their connections, and concludes with a brief account of related results, extensions and applications.