Dror Givon

Research Associate
The Program in Applied and Computational Mathematics
and the Department of Chemical Engineering
Princeton University

Research Interests

• Numerical Analysis, Computational Mathematics
  
• Multiscale Analysis of Stochastic Processes:
  
• Equation - Free computations and Multiscale Integrators
  • Agent based computations, analysis, simulation of large population of neurons
  • The Median Principle
  • Parallel Computations (currently on the Linux Clusters here in Princeton)
  • Data Mining - through Diffusion Maps
• Optimal Prediction, Variable reduction,
• Particle Filtering applied to systems of ODEs, SDEs, Jump processes, Jump - Diffusions,
• Polynomial Chaos and uncertainty quantification

Publications and preprints

• Coarse-grained projective schemes for certain singularly perturbed stochastic problems
  D. Givon and I. Kevrekidis
  submitted to SIAM Journal on Scientific Computing
• Multiscale integration schemes for jump-diffusion processes
  D. Givon and I. Kevrekidis
  Multiscale Modeling and Simulation. Volume 7 Issue 2 Pages 495-516, 2008
• Variance Reduction for Particle Filters of Systems With Time Scale Separation
  D. Givon, P. Stinis and J. Weare
  IEEE Trans. Signal Proc, Vol 57, Issue 2, Pages 424 - 435, 2009
• Strong convergence rate for two-time-scale jump-diffusion stochastic differential systems
  D. Givon
  Multiscale Modeling and Simulation Volume 6 Issue 2 Pages 577-594 (2007)
• Strong convergence of projective integration schemes for singularly perturbed stochastic differential systems
  D. Givon, I. Kevrekidis and R. Kupferman
  Commun. Math. Sci. Volume 4, Number 4 (2006), 707-729
• Existence proof for orthogonal dynamics and the Mori-Zwanzig formalism
  Israel J. Math. 145 (2005), 221--241
  D. Givon, O. Hald and R. Kupferman
• Extracting macroscopic dynamics: model problems and algorithms
  D. Givon, R. Kupferman and A. Stuart
  INVITED ARTICLE, 2004 Nonlinearity 17 R55-R127 doi:10.1088/0951-7715/17/6/R01
• White noise limits for discrete dynamical systems driven by fast deterministic dynamics
  D. Givon and R. Kupferman
  Physica A: Statistical and Theoretical Physics Volume 335, Issues 3-4, 15 April 2004, Pages 385-412