The Experts below are selected from a list of 252 Experts worldwide ranked by ideXlab platform
Jeremie Unterberger - One of the best experts on this subject based on the ideXlab platform.
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stochastic calculus for fractional brownian motion with hurst exponent h a rough path method by Analytic Extension
Annals of Probability, 2009Co-Authors: Jeremie UnterbergerAbstract:The d-dimensional fractional Brownian motion (FBM for short) B t = ((B (1) t ,.., B (d) t ), t ∈ R) with Hurst exponent α, α ∈ (0, 1), is a d-dimensional centered, self-similar Gaussian process with covariance E[B (i) s B (i) t ] = 1 2 δi,j (lsl 2α + ltl 2α ― |t ― s | 2α ). The long-standing problem of defining a stochastic integration with respect to FBM (and the related problem of solving stochastic differential equations driven by FBM) has been addressed successfully by several different methods, although in each case with a restriction on the range of either d or α. The case α = ½ corresponds to the usual stochastic integration with respect to Brownian motion, while most computations become singular when α gets under various threshhold values, due to the growing irregularity of the trajectories as α → 0. We provide here a new method valid for any d and for α > 1/4 by constructing an approximation Γ(e) t , e → 0, of FBM which allows to define iterated integrals, and then applying the geometric rough path theory. The approximation relies on the definition of an Analytic process Γ z on the cut plane z ∈ C \ R of which FBM appears to be a boundary value, and allows to understand very precisely the well-known (see [5]) but as yet a little mysterious divergence of Levy's area for α → 1/4
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stochastic calculus for fractional brownian motion with hurst exponent h a rough path method by Analytic Extension
Annals of Probability, 2009Co-Authors: Jeremie UnterbergerAbstract:The d-dimensional fractional Brownian motion (FBM for short) Bt=((Bt(1), …, Bt(d)), t∈ℝ) with Hurst exponent α, α∈(0, 1), is a d-dimensional centered, self-similar Gaussian process with covariance ${\mathbb{E}}[B_{s}^{(i)}B_{t}^{(j)}]=\frac{1}{2}\delta_{i,j}(|s|^{2\alpha}+|t|^{2\alpha}-|t-s|^{2\alpha})$. The long-standing problem of defining a stochastic integration with respect to FBM (and the related problem of solving stochastic differential equations driven by FBM) has been addressed successfully by several different methods, although in each case with a restriction on the range of either d or α. The case α=½ corresponds to the usual stochastic integration with respect to Brownian motion, while most computations become singular when α gets under various threshhold values, due to the growing irregularity of the trajectories as α→0. We provide here a new method valid for any d and for α>¼ by constructing an approximation Γ(ɛ)t, ɛ→0, of FBM which allows to define iterated integrals, and then applying the geometric rough path theory. The approximation relies on the definition of an Analytic process Γz on the cut plane z∈ℂ∖ℝ of which FBM appears to be a boundary value, and allows to understand very precisely the well-known (see [5]) but as yet a little mysterious divergence of Levy’s area for α→¼.
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stochastic calculus for fractional brownian motion with hurst exponent h 1 4 a rough path method by Analytic Extension
arXiv: Probability, 2007Co-Authors: Jeremie UnterbergerAbstract:The $d$-dimensional fractional Brownian motion (FBM for short) $B_t=((B_t^{(1)},...,B_t^{(d)}),t\in\mathbb{R})$ with Hurst exponent $\alpha$, $\alpha\in(0,1)$, is a $d$-dimensional centered, self-similar Gaussian process with covariance ${\mathbb{E}}[B_s^{(i)}B _t^{(j)}]={1/2}\delta_{i,j}(|s|^{2\alpha}+|t|^{2\alpha}-|t-s|^{2 \alpha}).$ The long-standing problem of defining a stochastic integration with respect to FBM (and the related problem of solving stochastic differential equations driven by FBM) has been addressed successfully by several different methods, although in each case with a restriction on the range of either $d$ or $\alpha$. The case $\alpha={1/2}$ corresponds to the usual stochastic integration with respect to Brownian motion, while most computations become singular when $\alpha$ gets under various threshhold values, due to the growing irregularity of the trajectories as $\alpha\to0$. We provide here a new method valid for any $d$ and for $\alpha>{1/4}$ by constructing an approximation $\Gamma(\varepsilon)_t$, $\varepsilon\to0$, of FBM which allows to define iterated integrals, and then applying the geometric rough path theory. The approximation relies on the definition of an Analytic process $\Gamma_z$ on the cut plane $z\in\mathbb{C}\setminus\mathbb{R}$ of which FBM appears to be a boundary value, and allows to understand very precisely the well-known (see \citeCQ02) but as yet a little mysterious divergence of L\'evy's area for $\alpha\to{1/4}$.
Robert B Hammond - One of the best experts on this subject based on the ideXlab platform.
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second order Analytic Extension of eigenvalues for fast frequency sweep analysis of rf circuits
IEEE Transactions on Microwave Theory and Techniques, 2021Co-Authors: Jianming Jin, Douglas R Jachowski, Robert B HammondAbstract:A second-order Analytic Extension of eigenvalue (AEE) method is presented and investigated for efficiently computing the ${Z}$ - parameters of passive RF circuits over a wide frequency band with full-wave accuracy. The ${Z}$ - parameters of an RF circuit are first extracted based on a full-wave simulation on sampling frequencies and then decomposed into eigenmodes, whose eigenvalues are Analytically extended to all other frequencies within the frequency band of interest based on functional equations constructed from second-order series and parallel $RLC$ circuits. An eigenvector-eigenvalue identity is adopted to compute the frequency-dependent eigenvectors from the eigenvalues of the submatrices, which are used in the expansion of the ${Z}$ - parameters. A comparison with full-wave solutions is given for the second-order AEE where four frequencies are employed to accurately approximate the ${Z}$ - parameters and predict the frequency response over the entire band of interest that goes to much higher frequencies than the first-order AEE. With this, the previously developed first-order AEE for a quasi-static analysis is successfully extended to much higher frequencies. Numerical examples are provided to validate the accuracy and demonstrate the capability of the second-order AEE. It is found that the second-order AEE is very accurate for modeling RF circuits with electrical sizes up to one wavelength that possibly contains resonances, as compared to the first-order AEE, which is applicable only to RF circuits with electrical sizes smaller than one-tenth to one-fifth of a wavelength that contains no resonance.
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fast frequency sweep analysis of passive miniature rf circuits based on Analytic Extension of eigenvalues
IEEE Transactions on Microwave Theory and Techniques, 2021Co-Authors: Jianming Jin, Douglas R Jachowski, Robert B HammondAbstract:A fast frequency sweep approach based on Analytic Extension of eigenvalues (AEE) is presented and investigated for an efficient analysis of miniature passive RF circuits. In this approach, an eigenvalue decomposition is performed to the Z-parameters of the circuit components at one or a few frequencies, and Analytic Extension is applied to obtain the eigenvalues at all other frequencies within the band of interest. For electrically small circuit components, the frequency-independent characteristic inductances and capacitances, as well as the frequency-dependent resistances, are extracted from the eigenvalues at the sampling frequencies. The extracted characteristic parameters are then used to approximate the Z- and Y-parameters and predict the responses of the circuit over the entire frequency band. The accuracy of this approach is evaluated by comparing it with the results from a full-wave analysis. It is found that the proposed AEE is very accurate with a relative error of less than 1% for miniature RF circuits whose electrical sizes are smaller than one tenth of the wavelength and is more general and powerful than the one based on lumped equivalent circuits.
Jianming Jin - One of the best experts on this subject based on the ideXlab platform.
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second order Analytic Extension of eigenvalues for fast frequency sweep analysis of rf circuits
IEEE Transactions on Microwave Theory and Techniques, 2021Co-Authors: Jianming Jin, Douglas R Jachowski, Robert B HammondAbstract:A second-order Analytic Extension of eigenvalue (AEE) method is presented and investigated for efficiently computing the ${Z}$ - parameters of passive RF circuits over a wide frequency band with full-wave accuracy. The ${Z}$ - parameters of an RF circuit are first extracted based on a full-wave simulation on sampling frequencies and then decomposed into eigenmodes, whose eigenvalues are Analytically extended to all other frequencies within the frequency band of interest based on functional equations constructed from second-order series and parallel $RLC$ circuits. An eigenvector-eigenvalue identity is adopted to compute the frequency-dependent eigenvectors from the eigenvalues of the submatrices, which are used in the expansion of the ${Z}$ - parameters. A comparison with full-wave solutions is given for the second-order AEE where four frequencies are employed to accurately approximate the ${Z}$ - parameters and predict the frequency response over the entire band of interest that goes to much higher frequencies than the first-order AEE. With this, the previously developed first-order AEE for a quasi-static analysis is successfully extended to much higher frequencies. Numerical examples are provided to validate the accuracy and demonstrate the capability of the second-order AEE. It is found that the second-order AEE is very accurate for modeling RF circuits with electrical sizes up to one wavelength that possibly contains resonances, as compared to the first-order AEE, which is applicable only to RF circuits with electrical sizes smaller than one-tenth to one-fifth of a wavelength that contains no resonance.
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fast frequency sweep analysis of passive miniature rf circuits based on Analytic Extension of eigenvalues
IEEE Transactions on Microwave Theory and Techniques, 2021Co-Authors: Jianming Jin, Douglas R Jachowski, Robert B HammondAbstract:A fast frequency sweep approach based on Analytic Extension of eigenvalues (AEE) is presented and investigated for an efficient analysis of miniature passive RF circuits. In this approach, an eigenvalue decomposition is performed to the Z-parameters of the circuit components at one or a few frequencies, and Analytic Extension is applied to obtain the eigenvalues at all other frequencies within the band of interest. For electrically small circuit components, the frequency-independent characteristic inductances and capacitances, as well as the frequency-dependent resistances, are extracted from the eigenvalues at the sampling frequencies. The extracted characteristic parameters are then used to approximate the Z- and Y-parameters and predict the responses of the circuit over the entire frequency band. The accuracy of this approach is evaluated by comparing it with the results from a full-wave analysis. It is found that the proposed AEE is very accurate with a relative error of less than 1% for miniature RF circuits whose electrical sizes are smaller than one tenth of the wavelength and is more general and powerful than the one based on lumped equivalent circuits.
Mokdad Mokdad - One of the best experts on this subject based on the ideXlab platform.
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reissner nordstrom de sitter manifold photon sphere and maximal Analytic Extension
Classical and Quantum Gravity, 2017Co-Authors: Mokdad MokdadAbstract:This paper is devoted to the study of Reissner–Nordstrom–de Sitter black holes and their maximal Analytic Extensions. Here, we find the necessary and sufficient conditions on the parameters of the Reissner–Nordstrom–de Sitter metric—namely, the mass, the charge, and the cosmological constant—to have three horizons. Under these conditions, we prove that there is only one photon sphere and we locate it. We then give a detailed construction of the maximal Analytic Extension of the Reissner–Nordstrom–de Sitter manifold in the case of three horizons. Studying these properties lays the groundwork for obtaining (in separate papers) decay results (Mokdad 2017 Decay of Maxwell fields on Reissner–Nordstrom–de Sitter black holes (arXiv:1704.06441)) and constructing conformal scattering theories for test fields on such spacetimes (Mokdad 2017 Conformal scattering of Maxwell fields on Reissner–Nordstrom–de Sitter black hole spacetimes (arXiv:1706.06993)).
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reissner nordstr o m de sitter manifold photon sphere and maximal Analytic Extension
arXiv: Differential Geometry, 2017Co-Authors: Mokdad MokdadAbstract:This paper is devoted to the study of the Reissner-Nordstr{\o}m-de Sitter black holes and their maximal Analytic Extensions. In particular, we study some of their properties that lays the groundwork for separate papers where we obtain decay results and construct conformal scattering theories for test fields on such spacetimes. Here, we find the necessary and sufficient conditions on the parameters of the Reissner-Nordstr{\o}m-de Sitter metric -namely, the mass, the charge, and the cosmological constant- to have three horizons. Under this conditions, we prove that there is only one photon sphere and we locate it. We then give a detailed construction of the maximal Analytic Extension of the Reissner-Nordstr{\o}m-de Sitter manifold in the case of three horizons.
Douglas R Jachowski - One of the best experts on this subject based on the ideXlab platform.
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second order Analytic Extension of eigenvalues for fast frequency sweep analysis of rf circuits
IEEE Transactions on Microwave Theory and Techniques, 2021Co-Authors: Jianming Jin, Douglas R Jachowski, Robert B HammondAbstract:A second-order Analytic Extension of eigenvalue (AEE) method is presented and investigated for efficiently computing the ${Z}$ - parameters of passive RF circuits over a wide frequency band with full-wave accuracy. The ${Z}$ - parameters of an RF circuit are first extracted based on a full-wave simulation on sampling frequencies and then decomposed into eigenmodes, whose eigenvalues are Analytically extended to all other frequencies within the frequency band of interest based on functional equations constructed from second-order series and parallel $RLC$ circuits. An eigenvector-eigenvalue identity is adopted to compute the frequency-dependent eigenvectors from the eigenvalues of the submatrices, which are used in the expansion of the ${Z}$ - parameters. A comparison with full-wave solutions is given for the second-order AEE where four frequencies are employed to accurately approximate the ${Z}$ - parameters and predict the frequency response over the entire band of interest that goes to much higher frequencies than the first-order AEE. With this, the previously developed first-order AEE for a quasi-static analysis is successfully extended to much higher frequencies. Numerical examples are provided to validate the accuracy and demonstrate the capability of the second-order AEE. It is found that the second-order AEE is very accurate for modeling RF circuits with electrical sizes up to one wavelength that possibly contains resonances, as compared to the first-order AEE, which is applicable only to RF circuits with electrical sizes smaller than one-tenth to one-fifth of a wavelength that contains no resonance.
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fast frequency sweep analysis of passive miniature rf circuits based on Analytic Extension of eigenvalues
IEEE Transactions on Microwave Theory and Techniques, 2021Co-Authors: Jianming Jin, Douglas R Jachowski, Robert B HammondAbstract:A fast frequency sweep approach based on Analytic Extension of eigenvalues (AEE) is presented and investigated for an efficient analysis of miniature passive RF circuits. In this approach, an eigenvalue decomposition is performed to the Z-parameters of the circuit components at one or a few frequencies, and Analytic Extension is applied to obtain the eigenvalues at all other frequencies within the band of interest. For electrically small circuit components, the frequency-independent characteristic inductances and capacitances, as well as the frequency-dependent resistances, are extracted from the eigenvalues at the sampling frequencies. The extracted characteristic parameters are then used to approximate the Z- and Y-parameters and predict the responses of the circuit over the entire frequency band. The accuracy of this approach is evaluated by comparing it with the results from a full-wave analysis. It is found that the proposed AEE is very accurate with a relative error of less than 1% for miniature RF circuits whose electrical sizes are smaller than one tenth of the wavelength and is more general and powerful than the one based on lumped equivalent circuits.