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Stochastic differential equations

Course description


Introduction to stochastic differential equations

Syllabus


  1. Introduction and motivations
  2. Brownian motion
  3. Stochastic integrals, Ito formula
  4. Stochastic differential equations
  5. Applications

Example


Probabilistic approximation of the solution of the Dirichlet problem {Δu=0in Eu=gfor ∂E

(∀x∈E)u(x)=E(g(Xτx)) where Xt is a brownian motion starting at x∈E and τx is the time when Xt reaches ∂E.

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