About

Raya Feldman is an Associate Professor in the Department of Statistics and Applied Probability at the University of California, Santa Barbara. She holds a Doctor of Science (DSc) degree from Technion in Haifa, Israel. Her research focuses on probability theory, stochastic processes, time series, and signal processing. She is based in South Hall at UCSB and can be contacted via email at feldman@pstat.ucsb.edu or by phone at (805) 893-2826.

Research topics

• Mathematics
• Statistical physics
• Statistics
• Mathematical analysis
• Computer science

Selected publications

• Limit Distributions for Sums of Independent Random Vectors

  Journal of the American Statistical Association · 2002-09-01 · 166 citations

  article1st authorCorresponding

  "Limit Distributions for Sums of Independent Random Vectors." Journal of the American Statistical Association, 97(459), pp. 925–926

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• A Course in Probability Theory

  Journal of the American Statistical Association · 2002-06-01 · 582 citations

  article1st authorCorresponding

  "A Course in Probability Theory." Journal of the American Statistical Association, 97(458), pp. 658–659

  PublisherDOI

• A Practical Guide to Heavy Tails: Statistical Techniques and Applications

  Journal of the American Statistical Association · 1999-06-01 · 646 citations

  article

  Part 1 Applications: heavy tailed probability distributions in the World Wide Web, M.E. Crovella et al self-similarity and heavy tails - structural modelling of network traffic, W. Willinger et al heavy tails in high-frequency financial data, U.A. Muller et al stable paretian modelling in finance - some empirical and theoretical aspects, S. Mittnik et al risk management and quantile estimation, F. Bassi et al. Part 2 Time series: analyzing stable time series, R.J. Adler et al inference for linear processes with stable noise, m. Calder, R.A. Davis on estimating the intensity of long-range dependence in finite and infinite variance time series, M.S. Taqqu, V. Teverovsky why non-linearities can ruin the heavy tailed modeller's day, S.I. Resnick periodogram estimates from heavy-tailed data, T. Mikosch Bayesian inference for time series with infinite variance stable innovations, N. Ravishanker, Z. Qiou. Part 3 Heavy tail estimation: hill, bootstrap and jackknife estimators for heavy tails, O.V. Pictet et al characteristic function based estimation of stable distribution parameters, S.M. Kogan. D.B. Williams. Part 4 Regression: bootstrapping signs and permutations for regression with heavy tailed errors - a robust resampling, R. LePage et al linear regression with stable disturbances, J.H. McCulloch. Part 5 Signal processing: deviation from normality in statistical signal processing - parameter estimation with alpha-stable distributions, P. Tsakalides, C.L. Nikias statistical modelling and receiver design for multi-user communication networks, G.A. Tsihrintzis. Part 6 Model structures: subexponential distributions, C.M. Goldie, C. Kluppelberg structure of stationary stable processes, J. Rosinski tail behaviour of some shot noise processes, G. Samorodnitsky. Part 7 Numerical procedures: numerical approximation of the symmetric stable distribution and density, J.H. McCulloch table of the maximally-skewed stable distributions, J.H. McCulloch, D.B. Panton multivariate stable distributions - approximation, estimation, simulation and identification, J.P. Nolan univariate stable distributions -parametrizations and software, J.P. Nolan.

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• Optimal Filtering of a Gaussian Signal in the Presence of Lévy Noise

  SIAM Journal on Applied Mathematics · 1999-01-01 · 16 citations

  articleSenior author

  Many engineering applications require extracting a signal from observations corrupted by additive noise, possibly heavy-tailed. We assume that the observation noise is a Lévy process, while the signal is Gaussian, and derives a nonlinear recursive filter that minimizes the L2 error. A suboptimal filter is proposed for numerical purposes, and simulations show that it outperforms the existing linear filter.

  PublisherDOI

• Non-Gaussian Density Processes Arising from Non-Poisson Systems of Independent Brownian Motions

  Journal of Applied Probability · 1998-03-01

  article1st authorCorresponding

  The Brownian density process is a Gaussian distribution-valued process. It can be defined either as a limit of a functional over a Poisson system of independent Brownian particles or as a solution of a stochastic partial differential equation with respect to Gaussian martingale measure. We show that, with an appropriate change in the initial distribution of the infinite particle system, the limiting density process is non-Gaussian and it solves a stochastic partial differential equation where the initial measure and the driving measure are non-Gaussian, possibly having infinite second moment.

  PublisherDOI

• Non-Gaussian Density Processes Arising from Non-Poisson Systems of Independent Brownian Motions

  Journal of Applied Probability · 1998-03-01 · 2 citations

  article1st authorCorresponding

  The Brownian density process is a Gaussian distribution-valued process. It can be defined either as a limit of a functional over a Poisson system of independent Brownian particles or as a solution of a stochastic partial differential equation with respect to Gaussian martingale measure. We show that, with an appropriate change in the initial distribution of the infinite particle system, the limiting density process is non-Gaussian and it solves a stochastic partial differential equation where the initial measure and the driving measure are non-Gaussian, possibly having infinite second moment.

  PublisherDOI

• Analysing Stable Time Series

  1997-01-01 · 36 citations

  report

  We describe how to take a stable, ARMA, time series through the various stages of model identi cation, parameter estimation, and diagnostic checking, and accompany the discussion with a goodly number of large scale simulations that show which methods do and do not work, and where some of the pitfalls and problems associated with stable time series modelling lie. 1.

  PublisherDOI

• A Practical Guide to Heavy Tails: Statistical Techniques for Analyzing Heavy Tailed Distributions

  1997-01-01 · 197 citations

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  PublisherDOI

• Predicting Speedup for Distributed Computing on a Token Ring Network

  Journal of Parallel and Distributed Computing · 1997-08-01 · 5 citations

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  PublisherDOI

• A representation for functionals of superprocesses via particle picture

  Stochastic Processes and their Applications · 1996-11-01 · 5 citations

  article1st authorCorresponding
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Frequent coauthors

• Srikanth K. Iyer

  6 shared

• Robert J. Alder

  Israel Institute

  2 shared

• David B. Kim

  University of California, Santa Barbara

  1 shared

• Nagamani Krishnakumar

  University of California, Santa Barbara

  1 shared

• Russell V. Lenth

  1 shared

• Svetlozar T. Rachev

  Texas Tech University

  1 shared

• Marica Lewin

  Technion – Israel Institute of Technology

  1 shared

• Murad S. Taqqu

  Boston University

  1 shared

Labs

• Center for Financial Mathematics and Actuarial ResearchPI