Ashot Nikolaevich Agadzhanov

Ph.D., Senior Scientist of Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia.

Group Leader of   Scientific Research and Software Development Group Stochastica

Contact information:

Institute of Control Sciences, Russian Academy of Sciences, Profsoyusnaya str., 65, 117806 Moscow, Russia.
E-mail: ashot@stochastica.org

 


Research themes

  • Functional Analysis
    • Sobolev spaces of infinite order
    • Geometry of Banach spaces (uniform convexity and smoothness, superreflexivity, stochastic methods in Banach spaces)
    • Bases in Banach spaces
    • Monotone and coercive operators in Banach spaces (with reference to differential equations of infinite order), monotone limits of Banach spaces
    • Interpolation and compact embedding of Banach spaces. Approximation numbers
    • Frechet nuclear spaces
    • Nonlinear stochastic differential equations of Ito type
  • Function theory
    • Quasianalytic classes of functions
    • Special classes of functions. Bessel functions. Orthogonal polynomials. Walsh functions. Haar functions
    • Contiguous nowhere differentiable functions
    • Fractal curves
    • Cantor sets. Singular functions
    • Fractional calculus and its applications
  • Theory of probability and mathematical statistics
    • Singular distributions
    • Stable distributions
    • Monte Carlo methods
    • Robust statistical methods
  • Computing mathematics
    • The development of numerical methods of improved accuracy for the solution of differential equations, systems and integral equations
    • The development of effective robust numerical methods of nonparametric density estimation of stationary stochastic processes on finite samples
    • The development of effective robust numerical estimations of power spectral density, correlation function, higher order spectra of stationary stochastic processes on finite samples
    • The development of effective robust numerical estimations of fractional order statistics of stationary stochastic processes on finite samples
    • The development of effective robust numerical estimations of autoregressive type model parameters of stationary stochastic processes on finite samples
    • The development of effective robust numerical estimations of change point detection and estimation of stationary stochastic processes on finite samples
    • The development of effective algorithms for the numerical evaluation of fractional derivatives


Top

Publications

  • Stochastic Sobolev Spaces of Infinite Order and their Applications to the Solvability of Operator Equations, Scientific Conference Proceedings of Moscow Power Engineering Institute: Computer Engineering and Computing Systems, 1985
  • Stochastic Sobolev Spaces of Infinite Order. Non-triviality Criteria, Moscow Power Engineering Institute Proceedings, No. 45, pp. 119-121, 1986
  • Functional Properties of Sobolev Spaces of Infinite Order, Sov. Math., Dokl. 38, No.1, 88-92 (1989); translation from Dokl. Akad. Nauk SSSR 301, No.3, 521-524 (1988).
  • Nonlinear Stochastic Equations of Infinite Order and Corresponding Functional Spaces, Uspekhi Mat. Nauk, vol. 43, 1988
  • Modern Statistical Methods of Measuring Information Processing, Center For Scientific and Technical Information "Poisk", Moscow, 1988.
  • Modern Statistical Methods of Measuring Information Processing, Center For Scientific and Technical Information "Poisk", Moscow, 1989.
  • Modern Statistical Methods of Change Detection in Probabilistic Characteristic of Stochastic Processes, Center for Scientific and Technical Information "Poisk", Moscow, 1990.
  • Strictly Nuclear Imbeddings and Interpolation of Sobolev Spaces of Infinite Order, Sov. Math., Dokl. 43, No.1, 108-111 (1991); translation from Dokl. Akad. Nauk SSSR 316, No.3, 521-524 (1991).
  • Properties of Monotone Limits of Banach Spaces, Sov. Math., Dokl. 44, No.1, 247-251 (1992); translation from Dokl. Akad. Nauk SSSR 319, No.5, 1033-1036 (1991).
  • Nonlinear Stochastic Equations of Infinite Order and Corresponding Functional Spaces, Ph.D. Thesis, Moscow Power Engineering Institute, 1992
  • Autoregressive Models of Random Signals and their Application for Moving Object Detection, (with L.I. Weiss and M.U. Vinokurov), Proceedings of Institute of Control Sciences, Russian Academy of Sciences, No.1, Moscow, 1993.
  • Singular Probability Distributions and Chaos in Dynamic Systems, (with L.I. Weiss), Report of Institute of Control Sciences, Russian Academy of Sciences, Moscow, 1997.
  • Singular Probability Distributions and Chaos in Dynamic Systems, (with L.I. Weiss), Proceedings on International Conference on Control Problems, Moscow, 1999.
  • Probability Density Estimation, (with A.N. Kalashyan), Proceedings on International Conference on Control Problems, Moscow, 1999
  • Singular Probability Distributions, (with L.I. Weiss), Institute of Control Sciences, Russian Academy of Sciences, Preprint, Moscow, 1999.
  • Triangle Algebra, Tutorial, Moscow, 2000
  • Cantor Structures and Singular Probability Distributions, (with L.I. Weiss), Institute of Control Sciences, Russian Academy of Sciences, Preprint, Moscow (accepted for publication)
  • Parallel Computations of Distribution Functions with Singular Components, (with L.I. Weiss), International Conference "Parallel Computations and Control Sciences", Moscow, 2001.Top