Introduction to Stochastic Differential Equations: Theory and Numerics

What it is about

You learn the fundamentals of stochastic differential equations (SDEs) as well as their numerical treatment. By the end you will know the most important stochastic processes, the construction of stochastic integrals, and solution methods for SDEs, and you can analytically solve simple SDEs and apply numerical schemes to approximate general SDEs.

What you will be able to do

• Understand basic concepts of stochastic processes and Markov chains
• Be able to classify Wiener process and white noise
• Apply stochastic integration as well as Itô and Stratonovich calculus
• Formulate SDEs and explicitly solve simple SDEs
• Follow stochastic Taylor expansion
• Understand the Fokker–Planck equation
• Apply numerical methods for SDEs (strong/weak)
• Use Variance-Reduction methods and Stochastic Runge-Kutta methods

What the module consists of

• VorlesungIntroduction to theory, examples and applications; mathematical derivation of definitions and theorems

Teaching method

• VorlesungConcepts are presented with mathematical rigor (definition, theorem, proof); emphasis on applications and illustrative examples; some statements are given without proof