Research interests

Probability and its connections to Analysis, particularly Stochastic Analysis and Stochastic Partial differential Equations. Partial Differential Equations. Statistics.

Publications

• Preprints (papers below are available at http://arxiv.org, click on the titles below to see).

  1. N. Guerngar, E. Nane. On the well-posedness of space-time SPDEs with locally Lipschitz coefficients.

• Journal Publications

  1. N. Guerngar, E. Nane. Propagation of high peaks for the space-time fractional stochastic partial differential equations. Electron. J. Probab. 30 (2025), article no. 32, 1–22

  2. N.Guerngar, E. Nane, S. Ulusoy, H. W. van Wyk. A unique determination of the fractional exponents in a three-parameter fractional diffusion equation. Fractional Differential Calculus, Volume 13, Number 1 (2023), 87–104

  3. N. Guerngar, J. McCormick. Distributed-order space-time fractional diffusions in bounded domains. Discrete and Continuous Dynamical Systems - S, 2023, 16(10): 2783-2799. doi: 10.3934/dcdss.2023022

  4. N. Guerngar, E.Nane, R. Tinaztepe, S. Ulusoy, H. W. van Wyk. Simultaneous inversion for the fractional exponents in the space-time fractional diffusion equation ∂tβu=Δαu+Δγu. Frac. Calc. Appl. Anal, Vol 24, No. 3 (2021), pp. 818-847

  5. N. Guerngar, E. Nane. Moment bounds of a class of stochastic heat equation driven by space-time colored noise in bounded domains.
     Stoc. Proc. Appl. 130 (2020) 6246-6270.

  6. M. Foondun, N. Guerngar, E. Nane. Some properties of nonlinear fractional stochastic heat equation in bounded domains.
     Chaos, Solitons and Fractals, volume 102 (2017) 86-93.

Talks/Presentations

• Talks-Presentations

  1. Intermittency fronts of a class of space-time fractional heat equations driven by a space-time white noise, at the Organized Contributed Paper Session Qualitative Behavior of Stochastic Partial Differential Equations, the 11th World Congress in Probability and Statistics, August 12-16, 2024, Bochum, Germany

  2. Phase transition for Fractional Stochastic Partial Differential Equations in Bounded Domains at the University of Mississippi, Department of Mathematics' Probability & Statistics Seminar, November 9, 2023, Oxford, MS

  3. Moments and intermittent fonts for the space-time fractional stochastic diffusion equation at the special session on Stochastic Processes and Related Topics, the AMS 2023 Spring Southeastern Sectional Meeting, March 18-19, 2023, Georgia Tech, Atlanta, GA

  4. Some results about the fractional stochastic heat equation in bounded domains at the special session on Stochastic Analysis and Applications, the AMS 2021 Fall Southeastern Sectional Meeting, November 21, 2021, Virtual

  5. Some properties of the solution of SPDEs in bounded domains at the AMS Special Session on Orthogonal Polynomials, Quantum Probability, and Stochastic Analysis, the Joint Mathematics Meetings, January 13, 2018, San Diego, CA

  6. Support dose selection in oncology trials by predicting receptor occupancy, capstone project for team 5 at Math-to-Industry boot camp II, July 27, 2017, University of Minnesota Twin Cities, Minneapolis, MN

  7. Large time behavior for the solution of the fractional stochastic heat equation in bounded domains at the AMS Special Session on Stochastic Processes and Modeling, the Joint Mathematics Meetings, January 5, 2017, Atlanta, GA

  8. Large time behavior of the solution of SPDEs at the Auburn University, Department of Mathematics and Statistics Stochastic Seminar, December 1, 2016, Auburn, AL

  9. Inquiry Based Learning with Technology in Precalculus: Algebra (Poster presentation, co-authored with Dr. Regina Greiwe Jackson and X. Meng) at Auburn University's Conversations in Celebration of Teaching (CCT 2016), January 29, 2016, Auburn, AL

• Conferences Organized

  1. 11th World Congress of Probability and Statistics, Organized Contributed Paper Session Qualitative Behavior of Stochastic Partial Differential Equations, August 12-16, 2024, Bochum, Germany ( co-organized with Mohammud Foodun and Erkan Nane)

  2. AMS 2023 Spring Southeastern Sectional Meeting, Special Session on Stochastic Processes and Related Topics, March 18-19, 2023, Georgia Tech, Atlanta, GA (co-organized with Le Chen, Erkan Nane and Jerzy Szulga)

  3. AMS 2021 Fall Southeastern Sectional Meeting, Special Session on Stochastic Analysis and Applications, November 20-21, 2021, Virtual (co-organized with Le Chen and Erkan Nane)

• Related Conferences

  1. 11th World Congress of Probability and Statistics, August 12-16, 2024, Bochum, Germany

  2. 43rd Conference on Stochastic Processes and their Applications, July 24-28, 2023, Lisbon, Portugal

  3. Special Session on Stochastic Processes and Related Topics, the AMS 2023 Spring Southeastern Sectional Meeting, March 18-19, 2023, Georgia Tech, Atlanta, GA

  4. Special Session on Stochastic Analysis and Applications, the AMS 2021 Fall Southeastern Sectional Meeting, November 20-21, 2021, Virtual

  5. AMS 2019 Spring Southeastern Sectional Meeting, March 15-17, Auburn University, Auburn, AL

  6. AMS Special Session on Orthogonal Polynomials, Quantum Probability, and Stochastic Analysis, the Joint Mathematics Meetings, January 10-13, 2018, San Diego, CA

  7. Math-to-Industry boot camp II, the Institute of Mathematics and its Applications, July 27, 2017, University of Minnesota Twin Cities, Minneapolis, MN

  8. AMS Special Session on Stochastic Processes and Modeling, the Joint Mathematics Meetings, January 4-7, 2017, Atlanta, GA

  9. Stochastic Partial Differential Equations Workshop, Simons Center for Geometry and Physics, Stony Brook University, May 16-20, 2016, Stony Brook, NY

  10. Conversations in Celebration of Teaching (CCT 2016), January 29, 2016, Auburn University, Auburn, AL

  11. AMS 2015 Southeastern Sectional Meeting, University of Alabama in Huntsville, March 27-29, 2015, Huntsville, AL