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Dr. Kuldeep Kumar Kataria
Ph.D. (IIT Bombay)
Assistant Professor, IIT Bhilai
Department of Mathematics
kuldeepk@iitbhilai.ac.in

Areas of Interest

  • Probability Theory and Stochastic Processes.

Education

  • PhD, Indian Institute of Technology Bombay, 2018.
  • MSc, Indian Institute of Technology Kanpur, 2011.
  • BSc (Hons.), St. Stephen's College, University of Delhi, 2009.

Professional Experiences

  • Assistant Professor, Indian Institute of Technology Bhilai, Raipur, Dec 2018 -
  • NBHM Postdoctoral Fellow, Indian Institute of Science, Bangalore, July 2018 - Dec 2018.
  • Research Associate, Indian Institute of Technology Bombay, Mumbai, Dec 2017 - June 2018.

Teaching

  • MA611: Stochastic Processes
  • MA608: Martingale Theory
  • MA605: Operations Research
  • MA602: Differential Equations
  • MA503: Introduction to Probability Theory
  • MA504: Differential Equations
  • MA200: Differential Equations
  • IC152: Linear Algebra-II
  • IC105: Probability and Statistics

Administrative Responsibilities

  • Convener, DPGC, Sept 2020 -
  • Faculty In-charge, Student Mentorship Program, Jan 2020 - May 2021

Awards and Honours

  • Award of NBHM Postdoctoral Fellowship, 2018.
  • Award for "Excellence in Thesis Work" by Hon'ble Prime Minister of India at the 56th Convocation of IIT Bombay, 2018.
  • Qualified joint CSIR-UGC NET (JRF) three times consecutively in Mathematical Sciences, 2010-2011.
  • Qualified GATE (Graduate Aptitude Test in Engineering) two times consecutively in Mathematics, 2010-2011.
  • Qualified JAM (Joint Admission test to MSc) conducted by the IITs in Mathematics and Mathematical Statistics, 2009.
  • Award of Anu Bedi and KPMG fellowships by St. Stephen's College, University of Delhi, 2008-2009.

Published/Accepted Research Articles

  • Kataria, K. K. and Khandakar, M. (2022). Generalized fractional counting process. J. Theoret. Probab. https://doi.org/10.1007/s10959-022-01160-6
  • Kataria, K. K. and Khandakar, M. (2022). Extended eigenvalue-eigenvector method. Statist. Probab. Lett. 183, 109361.
  • Kataria, K. K., Vellaisamy, P. and Kumar, V. (2022). A probabilistic interpretation of the Bell polynomials. Stoch. Anal. Appl. 40(4), 610-622.
  • Kataria, K. K. and Khandakar, M. (2022). Time-changed space-time fractional Poisson process. Stoch. Anal. Appl. 40(2), 246-267.
  • Kataria, K. K. and Khandakar, M. (2021). Mixed fractional risk process. J. Math. Anal. Appl. 504(1), 125379.
  • Kataria, K. K. and Khandakar, M. (2021). Convoluted fractional Poisson process. ALEA, Lat. Am. J. Probab. Math. Stat. 18(2), 1241-1265.
  • Kataria, K. K. and Khandakar, M. (2021). On the long-range dependence of mixed fractional Poisson process. J. Theoret. Probab. 34(3), 1607–1622.
  • Ghosh S., Kataria, K. K. and Vellaisamy, P. (2021). On transmuted generalized linear exponential distribution. Comm. Statist. Theory Methods. 50(9), 1978-2000.
  • Kataria, K. K. and Vellaisamy, P. (2020). State dependent versions of the space-time fractional Poisson process. Fract. Calc. Appl. Anal. 23(5), 1483-1505.
  • Kataria, K. K. and Vellaisamy, P. (2019). On distributions of certain state dependent fractional point processes. J. Theoret. Probab. 32(3), 1554-1580.
  • Kataria, K. K. and Vellaisamy, P. (2019). On the convolution of Mittag-Leffler distributions and its applications to fractional point processes. Stoch. Anal. Appl. 37(1), 115-122.
  • Kataria, K. K. and Vellaisamy, P. (2018). On martingale characterizations for some generalized space fractional Poisson processes. Stoch. Anal. Appl. 36(4), 665-670.
  • Vellaisamy, P. and Kataria, K. K. (2018). The I-function distribution and its extensions. Theory Probab. Appl. 63(2), 227-245.
  • Kataria, K. K. and Vellaisamy, P. (2018). On densities of the product, quotient and power of independent subordinators. J. Math. Anal. Appl. 462(2), 1627-1643.
  • Kataria, K. K. and Vellaisamy, P. (2017). Correlation between Adomian and partial exponential Bell polynomials. C. R. Math. Acad. Sci. Paris 355(9), 929-936.
  • Kataria, K. K. and Vellaisamy, P. (2017). Saigo space-time fractional Poisson process via Adomian decomposition method. Statist. Probab. Lett. 129, 69-80.
  • Kataria, K. K. and Vellaisamy, P. (2016). Simple parametrization methods for generating Adomian polynomials. Appl. Anal. Discrete Math. 10(1), 168-185.
  • Kataria, K. K. and Vellaisamy, P. (2015). The generalized K-Wright function and Marichev-Saigo-Maeda fractional operators. J. Anal. 23, 75-87.
  • Kataria, K. K. and Vellaisamy, P. (2015). Some fractional calculus results associated with the I-function. Matematiche (Catania) 70(2), 173-190.

Published/Accepted Expository Articles

  • Kataria, K. K. and Mistri R. K. (2021). Generalized binomial theorem via Laplace transform technique. Math. Gaz. 105(564), 516-520.
  • Kataria, K. K. (2017). The binomial theorem procured from the solution of an ODE. Math. Mag. 90(5), 301-303.
  • Kataria, K. K. (2017). Some probabilistic interpretations of the multinomial theorem. Math. Mag. 90(3), 221-224.
  • Kataria, K. K. (2016). An alternate proof of the binomial theorem. Amer. Math. Monthly 123(9), 940.
  • Kataria, K. K. (2016). A probabilistic proof of the multinomial theorem. Amer. Math. Monthly 123(1), 94-96.

Chapters in Books/Edited Proceedings

  • Kataria, K. K. and Vellaisamy, P. (2019). Adomian Decomposition Method and Fractional Poisson Processes: A Survey, Edited by Varsha Daftardar-Gejji, Springer Proceedings.

Invited Talks/Conference/Summer Schools Participation

  • Invited colloquium talk on "On fractional counting processes" at Indian Institute of Science, Bangalore, January 2022.
  • Invited talk on "Subordinated stochastic processes and their applications", International Conference on Mathematical Techniques in Application of Science & Technology (ICMTAST-21) held at Dr. C.V. Raman University, Bilaspur, India during December 22–23, 2021.
  • Invited talk on "On fractional counting processes" at Indian Institute of Technology Bombay, November 2021.
  • Participated in the conference on "Advances in Stochastic Analysis for Handling Risks in Finance and Insurance" held in hybrid mode at Centre International de Rencontres Mathèmatiques, Marseille, France during September 13-17, 2021.
  • Participated in the 5th workshop on "Probability and Evolution" held in hybrid mode at Centre International de Rencontres Mathèmatiques, Marseille, France during June 28-July 02, 2021.
  • Invited talk on "Fractional Poisson models and their one dimensional distributions" in IISA 2019 Conference on Innovations in Data and Statistical Sciences (INDSTATS) held at Indian Institute of Technology Bombay, Mumbai, India during December 26-30, 2019.
  • Participated in the conference on "PDE/Probability Interactions: Particle Systems, Hyperbolic Conservation Laws" held at Centre International de Rencontres Mathèmatiques, Marseille, France during October 14-18, 2019.
  • Invited colloquium talk on "State dependent space time fractional point processes" at University of Hyderabad, July 2018.
  • Invited talk on "State dependent space time fractional point processes" at Indian Institute of Management Indore, June 2018.
  • Contributed talk on "Some recent results on Adomian polynomials: an integral part of Adomian decomposition method" in National Conference on Fractional Calculus and Fractional Differential Equations held at Savitribai Phule Pune University, Pune, India during November 6-8, 2017.
  • Participated in the summer school on "Spectral Properties of Large Random Objects" held at Institut des Hautes Etudes Scientifique, Paris, France during July 17-28, 2017.
  • Contributed talk on "Densities of stable and inverse stable subordinators" in Satellite Summer School to the 8th International Conference on Lèvy processes held at Universitè de Lille 1, Lille, France during July 18-22, 2016.

Review

  • Reviewed articles for Statistics & Probability Letters, Dependence Modeling, Mathematical Reviews, Mathematical Magazine, The Mathematics Student, Applied Mathematics E-Notes, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences.

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