Lingjiong Zhu


PhD in Mathematics,

Courant Institute, New York University, (2008-2013)

BA in Mathematics, University of Cambridge, (2005-2008)

Shanghai High School, (2002-2005)


Email Address

ling [at] cims [dot] nyu [dot] edu

zljxxw [at] hotmail [dot] com


I got my PhD in probability theory

under the supervision of Prof S. R. S. Varadhan.


Resume


Research Interests

My research interests lie in probability theory. During my PhD studies, I mainly worked on a wide class of point processes,

i.e. nonlinear Hawkes process, which is in general non-Markovian, self-exciting and has clustering effect.

I studied large deviations, central limit theorems and other limit theorems for Hawkes process as well as the tail behavior,

phase transitions for time asymptotics in different regimes and explosion criterion.

I also did some work on limit theorems for marked Hawkes processes, risk processes with subexponential claims,

large deviations for self-correcting point processes and monotonicity of the speed of biased random walks on Galton-Watson trees.




Research Papers

  1. Process-Level Large Deviations for Nonlinear Hawkes Point Processes, to appear in Annales de l’Institut Henri Poincaré, 2011, PDF

  2. Large Deviations for Markovian Nonlinear Hawkes Processes, submitted, 2011, PDF

  3. Central Limit Theorem for Nonlinear Hawkes Processes. (2013). Journal of Applied Probability, 50, 760-771. PDF

  4. Asymptotics for Nonlinear Hawkes Processes, in preparation

  5. Large Deviations for Self-Correcting Point Processes, in preparation, with Sanchayan Sen

  6. The Speed of a Biased Walk on a Galton-Watson Tree is Monotonic with Respect to Progeny Distributions for High Values of Bias, submitted, with Behzad Mehrdad and Sanchayan Sen, to appear in Annales de l’Institut Henri Poincaré, 2012, PDF

  7. Limit Theorems for Marked Hawkes Processes with Application to a Risk Model, submitted, with Dmytro Karabash, 2012, PDF

  8. Ruin Probabilities for Risk Processes with Non-Stationary Arrivals and Subexponential Claims. (2013). Insurance: Mathematics and Economics, 53, 544-550. PDF

  9. Moderate Deviations for Hawkes Processes. (2013) Statistics & Probability Letters, 83, 885-890.

  10. Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps, to appear in Journal of Applied Probability, PDF

  11. Limit Theorems for Empirical Density of Greatest Common Divisors, submitted, with Behzad Mehrdad, 2013, PDF

  12. Moderate and Large Deviations for Erdos-Kac Theorem, with Behzad Mehrdad, 2013, PDF

  13. Optimal Strategies for a Long-Term Static Investor, to appear in Stochastic Models, PDF

  14. Asymptotic Structure and Singularities in Constrained Directed Graphs, with David Aristoff, 2014, PDF

  15. On the Phase Transition Curve in a Directed Exponential Graph Model, with David Aristoff, 2014, PDF