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Quadratic variation and quadratic roughness
Bernoulli, 2023 We study the concept of quadratic variation of a continuous path along a sequence of partitions and its dependence with respect to the choice of the partition sequence. We define the concept of quadratic roughness of a path along a partition sequence and show that, for Hölder-continuous paths satisfying this roughness condition, the quadratic variation
Rama Cont
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On pathwise quadratic variation for càdlàg functions
Electronic Communications in Probability, 2018 arXiv admin note: text overlap with arXiv:1704 ...
Henry Chiu, Rama Cont
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On Quadratic Variation of Processes with Gaussian Increments
Annals of Probability, 1975 This note extends to a broad class of stochastic processes with Gaussian increments the following theorem of R. M. Dudley (Ann. Probability 1 66-103): if $\{\pi_n\}$ is any sequence of partitions of [0, 1] with mesh $(\pi_n) = o(1/\log n)$ and if $L(\pi_n)^2$ is the quadratic variation of Brownian motion corresponding to $\pi_n$, then a.s.-$\lim_{n ...
Evarist Gine
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Quadratic Variation and Semimartingales
Probability and Its Applications, 2015We now come to one of the key objects in stochastic analysis, and what fundamentally distinguishes the theory from classical calculus. This is the notion of the quadratic variation of a process.
Samuel N Cohen, Robert J Elliott
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Spectral characterization of the optional quadratic variation process [PDF]
Stochastic Processes and Their Applications, 1994 The authors prove some results on how to characterize the optional quadratic variation process via the periodogram of a semimartingale.
Peter Spreij
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Quadratic Variation of Functionals of Brownian Motion
Annals of Probability, 1977 The quadratic variation of functionals $F(t)$ of $n$-dimensional Brownian motion is investigated. Let $\Pi_n = \{t_1^n, t_2^n, \cdots, t^n_{l(n)}\}$ with $a = t_1^n < t_2^n < \cdots < t^n_{l(n)} = b$ be a family of partitions of the interval $\lbrack a, b\rbrack$. The limiting behavior of $Q^2(F, \Pi_n) = \sum^{l(n)-1}_{k=1} (F(t^n_{k+1}) - F(t_k^n))^2$
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Decomposition of Quadratic Variational Problems
2008Variational problems have proved of value in many image processing and analysis applications. However increase of sensor resolution as occurred in medical imaging and experimental fluid dynamics demand for adapted solving strategies to handle the huge amount of data.
Florian Becker, Christoph Schnörr
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Quadratic variation and structure of martingales
Lecture Notes in Mathematics, 1988Peter Imkeller
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1983
For the remainder of this book, we shall only consider integrators M which are continuous local martingales. By Proposition 1.9 these are automatically local L 2-martingales. A more extensive treatment, encompassing right continuous integrators would require more elaborate considerations which are not suitable for inclusion in this short book.
K. L. Chung, R. J. Williams
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For the remainder of this book, we shall only consider integrators M which are continuous local martingales. By Proposition 1.9 these are automatically local L 2-martingales. A more extensive treatment, encompassing right continuous integrators would require more elaborate considerations which are not suitable for inclusion in this short book.
K. L. Chung, R. J. Williams
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