Simulation of Stationary Gaussian Processes in [0,1] d

Wood, Andrew; Chan, Grace

doi:10.2307/1390903

Cited by 197 publications

(132 citation statements)

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“…56 We start the trajectory in the left well and record the waiting time when x(t) crosses over the bottom of the product well. For a barrier height E a ) 2k B T, barrier crossing events can be followed directly with reasonable computational times.…”

Section: Kramer's Barrier Crossing Problem Without Time Scale Separationmentioning

confidence: 99%

Fluctuating Enzymes: Lessons from Single-Molecule Studies

et al. 2005

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Recent single-molecule enzymology measurements with improved statistics have demonstrated that a single enzyme molecule exhibits large temporal fluctuations of the turnover rate constant at a broad range of time scales (from 1 ms to 100 s). The rate constant fluctuations, termed as dynamic disorder, are associated with fluctuations of the protein conformations observed on the same time scales. We discuss the unique information extractable from these experiments and the reconciliation of these observations with ensemble-averaged Michaelis-Menten equation. A theoretical model based on the generalized Langevin equation (GLE) treatment of Kramers' barrier crossing problem for chemical reactions accounts naturally for the observation of dynamic disorder and highly dispersed kinetics.

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Section: Kramer's Barrier Crossing Problem Without Time Scale Separationmentioning

confidence: 99%

Fluctuating Enzymes: Lessons from Single-Molecule Studies

et al. 2005

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“…It is of order N log N , i.e., even faster than the Hosking method. The method was later simultaneously generalized by Dietrich and Newsam [6] and Wood and Chan [16]. The algorithm is based on the fact that the covariance matrix of a stationary discrete-time Gaussian processes can be embedded in a so-called circulant matrix.…”

Section: Exact Simulation Of Fractional Brownian Motionmentioning

confidence: 99%

“…It should be noted that the Davies and Harte method can also be extended to higher dimensions [6,16].…”

Section: End Notes and Conclusionmentioning

confidence: 99%

On Spectral Simulation of Fractional Brownian Motion

Dieker¹,

Mandjes²

2003

Prob. Eng. Inf. Sci.

138

158

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C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a PNA Probability, Networks and Algorithms Probability, Networks and AlgorithmsOn spectral simulation of fractional Brownian motion . Despite the availability of several exact simulation methods, attention has been paid to approximate simulation (i.e., the output is approximately fBm), particularly because of possible time savings. In this paper, we study the class of approximate methods that are based on the spectral properties of fBm's stationary incremental process, usually called fractional Gaussian noise (fGn). The main contribution is a proof of asymptotical exactness (in a sense that is made precise) of these spectral methods. Moreover, we establish the connection between the spectral simulation approach and a widely used method, originally proposed by Paxson, that lacked a formal mathematical justification. The insights enable us to evaluate the Paxson method in more detail. It is also shown that spectral simulation is related to the fastest known exact method. Mathematics Subject Classification: 65C05, 62M15

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“…Among several existing algorithms, we adopt the simulation algorithm first mentioned by Davies and Harte (1987) and analyzed in Wood and Chan (1994), which is of order n log n for a sample size of n. With the Davies-Harte method, an fGn sample of size n can be constructed as follows. Note that this algorithm requires that n be a power of two:…”

Section: Simulation Of Fractional Brownian Motionmentioning

confidence: 99%

On Numerical Computation of Pickands Constants

Choi

2015

CSAM

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Pickands constant H α appears in the classical result about tail probabilities of the extremes of Gaussian processes and there exist several different representations of Pickands constant. However, the exact value of H α is unknown except for two special Gaussian processes. Significant effort has been made to find numerical approximations of H α . In this paper, we attempt to compute numerically H α based on its representation derived by Hüsler (1999) and Albin and Choi (2010). Our estimates are compared with the often quoted conjecture H α = 1/Γ(1/α) for 0 < α ≤ 2. This conjecture does not seem compatible with our simulation result for 1 < α < 2, which is also recently observed by Dieker and Yakir (2014) who devised a reliable algorithm to estimate these constants along with a detailed error analysis.

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Simulation of Stationary Gaussian Processes in [0,1] d

Cited by 197 publications

References 0 publications

Fluctuating Enzymes: Lessons from Single-Molecule Studies

Fluctuating Enzymes: Lessons from Single-Molecule Studies

On Spectral Simulation of Fractional Brownian Motion

On Numerical Computation of Pickands Constants

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