Stochastic Toolkit for Uncertainty Quantification in complex nonlinear systems
نویسنده
چکیده
1 Prliminaries 2 1.1 Basic Probability concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Stochastic Differential Equations (SDE’s) . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Langevin equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Ito integral and basics of Ito calculus . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.3 Path-wise solutions and statistics of the linear Langevin equation . . . . . . . . . . 8 1.3 Fokker-Planck equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
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