A Gaussian Approximation for Stochastic Nonlinear Dynamical Processes with Annihilation

Lecture slides:

• A Gaussian approximation for stochastic non-linear<br> dynamical processes with annihilation
• Contents
• Stochastic optimal control problem
• Hamilton-Jacobi-Bellman equation
• Log transformation and optimal control
• Fokker-Planck with decay
• A stochastic dynamical process with annihilation
• Relation with discrete time Kalman smoothing
• The transition density
• Path integral formulation
• Euler-Lagrange equations
• Euler-Lagrange equations01
• A formal forward-backward algorithm
• Numerical example
• Relation with classical mechanics (b = 0)
• Size of fluctuations: linear noise approximation
• Numerical example
• Partition function
• Partition function: numerical result
• Summary
• Discussion

Author: Wim Wiegerinck, Radboud University Nijmegen