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48
Analysis, Modeling and Generation of SelfSimilar VBR Video Traffic
, 1994
"... We present a detailed statistical analysis of a 2hour long empirical sample of VBR video. The sample was obtained by applying a simple intraframe video compression code to an action movie. The main findings of our analysis are (1) the tail behavior of the marginal bandwidth distribution can be accu ..."
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Cited by 468 (5 self)
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We present a detailed statistical analysis of a 2hour long empirical sample of VBR video. The sample was obtained by applying a simple intraframe video compression code to an action movie. The main findings of our analysis are (1) the tail behavior of the marginal bandwidth distribution can be accurately described using "heavytailed" distributions (e.g., Pareto); (2) the autocorrelation of the VBR video sequence decays hyperbolically (equivalent to longrange dependence) and can be modeled using selfsimilar processes. We combine our findings in a new (nonMarkovian) source model for VBR video and present an algorithm for generating synthetic traffic. Tracedriven simulations show that statistical multiplexing results in significant bandwidth efficiency even when longrange dependence is present. Simulations of our source model show longrange dependence and heavytailed marginals to be important components which are not accounted for in currently used VBR video traffic models. 1 I...
Rangebased estimation of stochastic volatility models
, 2002
"... We propose using the price range in the estimation of stochastic volatility models. We show theoretically, numerically, and empirically that rangebased volatility proxies are not only highly efficient, but also approximately Gaussian and robust to microstructure noise. Hence rangebased Gaussian qu ..."
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Cited by 125 (11 self)
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We propose using the price range in the estimation of stochastic volatility models. We show theoretically, numerically, and empirically that rangebased volatility proxies are not only highly efficient, but also approximately Gaussian and robust to microstructure noise. Hence rangebased Gaussian quasimaximum likelihood estimation produces highly efficient estimates of stochastic volatility models and extractions of latent volatility. We use our method to examine the dynamics of daily exchange rate volatility and find the evidence points strongly toward twofactor models with one highly persistent factor and one quickly meanreverting factor. VOLATILITY IS A CENTRAL CONCEPT in finance, whether in asset pricing, portfolio choice, or risk management. Not long ago, theoretical models routinely assumed constant volatility ~e.g., Merton ~1969!, Black and Scholes ~1973!!. Today, however, we widely acknowledge that volatility is both time varying and predictable ~e.g., Andersen and Bollerslev ~1997!!, andstochastic volatility models are commonplace. Discrete and continuoustime stochastic volatility models are extensively used in theoretical finance, empirical finance, and financial econometrics, both in academe and industry ~e.g., Hull and
Probability laws related to the Jacobi theta and Riemann zeta functions, and the Brownian excursions
 Bulletin (New series) of the American Mathematical Society
"... Abstract. This paper reviews known results which connect Riemann’s integral representations of his zeta function, involving Jacobi’s theta function and its derivatives, to some particular probability laws governing sums of independent exponential variables. These laws are related to onedimensional ..."
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Cited by 56 (12 self)
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Abstract. This paper reviews known results which connect Riemann’s integral representations of his zeta function, involving Jacobi’s theta function and its derivatives, to some particular probability laws governing sums of independent exponential variables. These laws are related to onedimensional Brownian motion and to higher dimensional Bessel processes. We present some characterizations of these probability laws, and some approximations of Riemann’s zeta function which are related to these laws. Contents
The SDE solved by local times of a Brownian excursion or bridge derived from the height profile of a random tree or forest
, 1997
"... Let B be a standard onedimensional Brownian motion started at 0. Let L t;v (jBj) be the occupation density of jBj at level v up to time t. The distribution of the process of local times (L t;v (jBj); v 0) conditionally given B t = 0 and L t;0 (jBj) = ` is shown to be that of the unique strong solu ..."
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Cited by 26 (7 self)
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Let B be a standard onedimensional Brownian motion started at 0. Let L t;v (jBj) be the occupation density of jBj at level v up to time t. The distribution of the process of local times (L t;v (jBj); v 0) conditionally given B t = 0 and L t;0 (jBj) = ` is shown to be that of the unique strong solution X of the Ito SDE dXv = n 4 \Gamma X 2 v \Gamma t \Gamma R v 0 Xudu \Delta \Gamma1 o dv + 2 p XvdBv on the interval [0; V t (X)), where V t (X) := inffv : R v 0 Xudu = tg, and Xv = 0 for all v V t (X). This conditioned form of the RayKnight description of Brownian local times arises from study of the asymptotic distribution as n !1 and 2k= p n ! ` of the height profile of a uniform rooted random forest of k trees labeled by a set of n elements, as obtained by conditioning a uniform random mapping of the set to itself to have k cyclic points. The SDE is the continuous analog of a simple description of a GaltonWatson branching process conditioned on its total progeny....
A Survey of Statistical Source Models for VariableBitRate Compressed Video
 Multimedia Systems
, 1999
"... . It is predicted that, in the near future, the transport of compressed video will pervade computer networks. Variablebitrate (VBR) encoded video is expected to become a significant source of network traffic, due to its advantages in statistical multiplexing gain and consistent video quality. Both ..."
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Cited by 22 (0 self)
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. It is predicted that, in the near future, the transport of compressed video will pervade computer networks. Variablebitrate (VBR) encoded video is expected to become a significant source of network traffic, due to its advantages in statistical multiplexing gain and consistent video quality. Both systems analysts and developers need to assess and study the impact these sources will have on their networks and networking products. To this end, suitable statistical source models are required to analyze performance metrics such as packet loss, delay and jitter. This paper provides a survey of VBR source models which can be used to drive network simulations. The models are categorized into four groups: Markov chain/linear regression, TES, selfsimilar and i.i.d/analytical. We present models which have been used for VBR sources containing moderatetosignificant scene changes and moderatetofull motion. A description of each model is given along with corresponding advantages and shortcom...
Fractal Character of the Neural Spike Train in the Visual System of the Cat
, 1997
"... d from one cell to the other or has a common origin. The gammar renewal process model, often used in the analysis of visualneuron interevent intervals, describes certain shortterm features of the RGC and LGN data reasonably well but fails to account for the longduration correlation. We present ..."
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Cited by 21 (4 self)
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d from one cell to the other or has a common origin. The gammar renewal process model, often used in the analysis of visualneuron interevent intervals, describes certain shortterm features of the RGC and LGN data reasonably well but fails to account for the longduration correlation. We present a new model for visualsystem nervespike firings: a gammar renewal process whose mean is modulated by fractal binomial noise. This fractal, doubly stochastic point process characterizes the statistical behavior of both RGC and LGN data sets remarkably well. 1997 Optical Society of America [S07403232(97)002020] 1. INTRODUCTION The sequence of action potentials recorded from cat retinal ganglion cells 116 (RGC's) and lateralgeniculatenucleus (LGN) cells 1721 remains irregular even when the retina is thoroughly adapted to a steady stimulus of fixed luminance. The statis
On the maximum drawdown of a Brownian motion
 J. Appl. Probab
"... If X(t) is a random process on [0, T], the maximum drawdown at time T, ¯ D(T), is defined by ¯D(T) = sup t∈[0,T] sup X(s) − X(t) s∈[0,t] Informally, this is the largest drop from a peak to a bottom. In this paper, we investigate the behavior of this statistic for a Brownian motion with drift. In ..."
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Cited by 7 (1 self)
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If X(t) is a random process on [0, T], the maximum drawdown at time T, ¯ D(T), is defined by ¯D(T) = sup t∈[0,T] sup X(s) − X(t) s∈[0,t] Informally, this is the largest drop from a peak to a bottom. In this paper, we investigate the behavior of this statistic for a Brownian motion with drift. In particular, we give an infinite series representation of its distribution, and consider its expected value. When the drift is zero, we give an analytic expression for the expected value, and for nonzero drift, we give an infinite series representation. For all cases, we compute the limiting (T → ∞) behavior, which can be
HURST EXPONENT AND FINANCIAL MARKET PREDICTABILITY
, 2007
"... The Hurst exponent (H) is a statistical measure used to classify time series. H=0.5 indicates a random series while H>0.5 indicates a trend reinforcing series. The larger the H value is, the stronger trend. In this paper we investigate the use of the Hurst exponent to classify series of financial ..."
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Cited by 5 (1 self)
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The Hurst exponent (H) is a statistical measure used to classify time series. H=0.5 indicates a random series while H>0.5 indicates a trend reinforcing series. The larger the H value is, the stronger trend. In this paper we investigate the use of the Hurst exponent to classify series of financial data representing different periods of time. Experiments with backpropagation Neural Networks show that series with large Hurst exponent can be predicted more accurately than those series with H value close to 0.50. Thus Hurst exponent provides a measure for predictability.
Chaining techniques and their application to stochastic flows
 In Trends in Stochastic Analysis, volume 353 of LMS Lecture Note Series
, 2009
"... We review several competing chaining methods to estimate the supremum, the diameter of the range or the modulus of continuity of a stochastic process in terms of tail bounds of their twodimensional distributions. Then we show how they can be applied to obtain upper bounds for the growth of bounded ..."
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Cited by 4 (2 self)
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We review several competing chaining methods to estimate the supremum, the diameter of the range or the modulus of continuity of a stochastic process in terms of tail bounds of their twodimensional distributions. Then we show how they can be applied to obtain upper bounds for the growth of bounded sets under the action of a stochastic flow. 1