Richard F. Gundy

Statistics Department
455 Hill Center
Rutgers University
Piscataway, NJ 08854-8019
Phone: 848-445-2690


A.B. 1955 Illinois College
Ph.D. 1960 Indiana University (Experimental Psychology)
Ph.D. 1966 University of Chicago (Statistics)

Present Position:

Professor of Statistics and Mathematics
Rutgers University
Piscataway NJ 08854

Previous Positions:

  • 1963-65 T. H. Hildebrandt Instructor, University of Michigan
  • 1965-66 Assistant Professor, Statistics, Rutgers University
  • 1966-70 Associate Professor, Statistics, Rutgers University
  • 1970- Professor, Statistics, Rutgers University
  • 1968-69 Visiting Professor, Rutgers Faculty Fellowship,
    The Hebrew University, Jerusalem, Israel
  • 1970-71 & (Fall Semester) Visiting Member, Institute Mittag-Leffler, Djursholm, Sweden
  • 1970-71 (Spring) Prof. d'change, Univ. of Paris, Orsay, France
  • 1974-75 & Rutgers Faculty Fellowship, Univ. of Paris, Orsay, France
  • 1977 & (Spring) Prof. d'echange, Univ. of Paris, Orsay, France
  • 1978-79 & FASP leave of absence; Univ. of Paris, Orsay, France
  • 1980 &(Spring) Overseas Fellow, Churchill College, Cambridge Univ.
  • 1981 & (Summer) Lecturer, Univ. of Texas
  • 1982 & Prof. d'echange, Univ. of Grenoble, Univ. of Paris
  • 1982-83 & Prof. Associe, Univ. of Paris (also supported by Faculty Fellowship Leave (Rutgers)
  • 1984 & (Spring) Prof. d'echange, Universite de Provence, Marseille, France
  • 1986 & (Spring) Visiting member, Institut d'Estudis Catalans, Centre de Recerca Matematica, Barcelona, Spain
  • 1986 & (March) Visiting member, Banach Institute, Warsaw, Poland
  • 1987 & (June-July) Prof. Associe, Universite de Clermont, Clermont-Ferrand, France
  • 1988 & ( May) Prof. Associe, Universite de Clermont, Clermont-Ferrand, France
  • 1990 & (February) Ecole normale sup. (Cachan)
  • 1990-91(March-Jan.) Institut Fourier, Universite de Grenoble
  • 1991 & (May-June) Universidad Central de Venezuela
  • 1991-92 & (Dec.-Jan) Lab. de Probabilites, Paris VI, Paris, France
  • 1993 & (Jan.) Universidad Central de Venezuela
  • 1994 & (May-August) Universidad Autonoma de Madrid (Sabbatical program supported by Spanish government)
  • 1997 & (May) Universidad Central de Venezuela

Professional Associations:

Fellow, Institute of Mathematical Statistics
Member of American Mathematical Society

Associate Editor:

Publicacions Mathematiques, Barcelona
Potential Analysis, Kluwer
Applied and Computational Harmonic Analysis, Academic Press

Invited Lectures:

American Mathematical Society, New York, April, 1979 "Recent developments in probability theory and classical analysis"
North British Functional Analysis Seminar, Edinburgh, Scotland; Principal Speaker, May, 1980
Midwest Conference on Real Analysis in Honor of A. Zygmund, March, 1981
Martingale Theory in Harmonic Analysis and Banach Spaces. Cleveland, Ohio, July, 1981
Conference Board on Mathematical Sciences; Principal Lecturer, DePaul University, Chicago, Illinois, July, 1986

Recent Invited Lectures:

AMS meeting on Probability Theory and Applications, Bloomington, Indiana, March, 1993
Kolmogorov semester, Euler International Mathematics Institute, St. Petersburg, Russia, March, 1993
Colloquium Speaker, Purdue University, March, 1993
Colloquium in Honor of Y. S. Chow, Columbia University, April, 1993
Invited Paper, AMS Meeting in Chicago, Ill., March, 1994
Principal Speaker, Journée d'Analyse ŕ l'honneur de Alain Bernard, Grenoble, France, June 1998.
Invited Paper, Annual Winter Meeting of the American Mathematical Society, San Antonio, January 1999.
Hour Lecture, AMS Regional Meeting, Urbana, Ill., March 1999.
Resource Person (Four Lectures), Sixth European Conference on Functional Analysis, Croatia, September 18-October 3, 1999.
Two lectures, Séminaire d'Analyse (Gilles Pisier), Paris VI, November 1999.
Conference on Harmonic and Stochastic Analysis, Northwestern University, June 2000.


  1. Completeness of L^2 and a Theorem of Renya, Michigan Math. J. 12 (1965), 161-167.
  2. Martingale Theory and the Pointwise Convergence of Certain Orthogonal Series, Trans. Amer. Math. Soc. 124 (2) (1966), 228-248.
  3. The Martingale Version of a Theorem of Marcinkiewicz and Zygmund, Ann. Math. Statist. 38 (3) (June) (1967), 725-734.
  4. On a Stopping Rule and the Central Limit Theorem (with David Siegmund), Ann. Math. Statist. 38 (6) (December) (1967), 915-917.
  5. On a Class of Martingale Series, Orthogonal Expansions and their Continuous Analogues, Edited by Deborah Tepper Haimo, Proceedings of the Conference held at Southern Illinois Univ., Edwardsville, April 27-29, 1967, pp.99-102.
  6. A Decomposition of L^1-Bounded Martingales, Ann. Math. Statist. 39 (1) (1968), 134-138.
  7. On the Class L*log L, Martingales, and Singular Integrals, Studia Math. 33, 109-118.
  8. Extrapolation and Interpolation of Quasi-Linear Operators on Martingales (with D. L. Burkholder), Acta Math. 124 (1970), 250-304.
  9. Integral Inequalities for Convex Functions of Operators on Martingales (with D. L. Burkholder and B. Davis), Proceedings of the Sixth Berkeley Symposium on Probability and Statistics, II, (1972), 230-240.
  10. A Maximal Function Characterization of the Class H^p (with D. L. Burkholder and M. L. Silverstein), Trans. Amer. Math. Soc. 157 (1971), 137-153.
  11. Distribution Function Inequalities for Certain Martingales, Seminaire d'analyse harmonique, Universite de Paris, Orsay, 1970-71.
  12. Distribution Function Inequalities for the Area Integral (with D. L. Burkholder), Studia Math. 44 (1972), 527-544.
  13. Boundary Behavior of Harmonic Functions in a Half-Space and Brownian Motion (with D. L. Burkholder), Ann. de l'Institut Fourier 23 (4) (1973).
  14. Weighted Integral Inequalities for the Nontangential Maximal Function, Lusin Area Integral, and Walsh-Paley Series (with R. L. Wheeden), Studia Math. 49 (1973), 101-118.
  15. A Martingale that Occurs in Harmonic Analysis (with N. Varopoulos), Ark. Math. 14 (2) (1976), 179-187.
  16. Local Convergence of a Class of Martingales in Multi-Dimensional Time, Ann. Prob. 8 (3) (1980), 607-614.
  17. Inegalities pour les Martingales a Un et Deux Indices, it Ecole d'ete, St. Flour, 1978. Lecture Notes in Math., #774, Springer-Verlag.
  18. H^p Spaces for the Bidisc (with E. M. Stein), it Proc. Nat. Acad. Sci. 76 (3) (1978), 106-109.
  19. Maximal Function Characterization of H^p for the Bidisc. Proceedings of the Conference on Harmonic Analysis, Iraklion, 1978. Lecture Notes in Math., #784, Springer-Verlag.
  20. Les Transformations de Riesz et les Integrales Stochastiques (with N. Th. Varapoulos), C. R. Acad. Sci. Paris 289 (2 juillet) (1979).
  21. Sur l'Integrabilite Uniform des Martingales (with J. Azema and M. Yor), Seminaire de Prob. XIV, 1978/79. Lecture Notes in Math., #784, pp.53-61, Springer-Verlag.
  22. On a Theorem of F. and M. Riesz and an Identity of A. Wald, Indiana J. Math. 30 (4) (1981).
  23. On a Probabilistic Interpretation of the Riesz Transforms (with M. L. Silverstein), Functional Analysis and Markov Processes, Kyoto, 1981; Lecture Notes in Math., #923, Springer-Verlag.
  24. On a Theorem of Kabanov, Lipster, and Shirayev (with G. K. Eagleson), Probability and Statistics, London. Math. Soc. Notes #79, pp.99-111, Cambridge Univ. Press, 1983.
  25. The Density of the Area Integral. Conference of Harmonic Analysis in Honor of A. Zygmund, vol. 1, Wadsworth, 1983, pp.138-149.
  26. Inequalities for Ratios of Functionals of Harmonic Functions (with R. Fefferman, M. Silverstein and E. M. Stein), Proc. Nat. Acad. Sci., USA 79 (1982), 7958-7960.
  27. Temps Locaux et l'Integrale d'Aire, in Seminaire de Prob., 1982/83. Springer-Verlag.
  28. The Density of the Area Integral in R_+^{n+1} (with M. Silverstein), Ann. de l'Institut Fourier 35 (1) (1985), 215-229.
  29. Sur les Transformations de Riesz Pour le Semi-Group d'Ornstein-Uhlenbeck, C. R. Acad. Sci. Paris 303 (Ser. I) (19) (1986).
  30. Topics in Probability and Analysis, Monograph for the Conference Board on Math Sciences Lecture Series, DePaul University, July, 1986.
  31. Some Martingale Inequalities with Applications to Harmonic Analysis J. Functional Analysis 87 (1) (1989), 212-230.
  32. Fonctionelles de variation quadratique et equations de dilatation (with I. Iribarren), C. R. Acad. Sci. Paris 317 (Ser. I) (1993), 333-336.
  33. 33. Distribution Function Inequalities for Quadratic Variation: A Survey, to appear in Proceedings of the Euler International Mathematical Institute, 1993.
  34. Quadratic Functionals and Dilation Equations (with I. Iribarren), Potential Analysis 4 (No. 5), October 1995, 503-519.
  35. Review of "A First Course on Wavelets," by E. Hernández and G. Weiss, CRC Press, Inc., 1996. SIAM Reviews 40 (June) (1998), 40-47.
  36. Stopping Times and Local Convergence of Spline Wavelet Expansions (with K. Kazarian). SIAM J. Math. Analysis 31 (3) (2000), 561-573.
  37. Stability Properties for a Compactly Supported Prescale Function (with V. Dobrić and P. Hitczenko). SIAM J. Math. Analysis 31 (3) (2000), 574-580.
  38. Characterizations of Orthonormal Scale Functions: A Probabilistic Approach (with V. Dobrić and P. Hitczenko). Journal of Geometric Analysis 10 (3) (2000), 413-430.
  39. Two Remarks on Wavelets: Cohen's Characterization for Low-Pass Filters, and Meyer's Theorem on Linear Independence, in Contemporary Math: The Harmonic and Functional Analysis of Wavelets. American Mathematical Society, #247, pp.249-257, Providence RI, 1999.
  40. Low-Pass Filters, Martingales, and Multiresolution Analyses. Applied and Computational Harmonic Analysis 9 (2) (2000), 204-219.
  41. Five lectures (Wavelets and Gaussian Processes,...) in Lecture Notes, Institut de Matemŕtica, Universitat de Barcelona, vol.1 (2002), pp. 125-215.
  42. Probability, Ergodic Theory, and Low-pass Filters. To appear in Proceedings of the International Conference on Harmonic Analysis and Ergodic Theory (in Honor of Marshall Ash and Roger Jones). DePaul University, Chicago IL, December 2005.