5 papers
Large deviations for the mean-field limit of Hawkes processes
Fuqing Gao, Lingjiong Zhu
Hawkes processes are a class of simple point processes whose intensity depends on the past history, and is in general non-Markovian. Limit theorems for Hawkes processes in various…
Privacy of SGD under Gaussian or Heavy-Tailed Noise: Guarantees without Gradient Clipping
Umut ÅimÅekli, Mert Gürbüzbalaban, Sinan Yıldırım +1
The injection of heavy-tailed noise into the iterates of stochastic gradient descent (SGD) has garnered growing interest in recent years due to its theoretical and empirical benefi…
Penalized Overdamped and Underdamped Langevin Monte Carlo Algorithms for Constrained Sampling
Mert Gürbüzbalaban, Yuanhan Hu, Lingjiong Zhu
We consider the constrained sampling problem where the goal is to sample from a target distribution when is constrained to lie on a convex body $\mathc…
Asymptotics for Short Maturity Asian Options in Jump-Diffusion models with Local Volatility
Dan Pirjol, Lingjiong Zhu
We present a study of the short maturity asymptotics for Asian options in a jump-diffusion model with a local volatility component, where the jumps are modeled as a compound Poisso…
Short-maturity asymptotics for option prices with interest rates effects
Dan Pirjol, Lingjiong Zhu
We derive the short-maturity asymptotics for option prices in the local volatility model in a new short-maturity limit at fixed , where is the interest ra…