Small random perturbation of ODE around hyperbolic points

SIAM Student Seminar
Friday, April 3, 2009 - 12:30pm for 2 hours
Skiles 269
Sergio Almada – School of Mathematics, Georgia Tech
Linwei Xin
Suppose b is a vector field in R^n such that b(0) = 0. Let A = Jb(0) the Jacobian matrix of b at 0. Suppose that A has no zero eigenvalues, at least one positive and at least one negative eigenvalue. I will study the behavior of the stochastic differential equation dX_\epsilon = b(X_\epsilon) + \epsilon dW as \epsilon goes to 0. I will illustrate the techniques done to deal with this kind of equation and make remarks on how the solution behaves as compared to the deterministic case.