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[ 404STCCSDEV23 ] VL (*)Stochastic Differential Equations
Versionsauswahl
(*) Leider ist diese Information in Deutsch nicht verfügbar.
Workload Ausbildungslevel Studienfachbereich VerantwortlicheR Semesterstunden Anbietende Uni
4,5 ECTS M - Master Mathematik Evelyn Buckwar 3 SSt Johannes Kepler Universität Linz
Detailinformationen
Quellcurriculum Masterstudium Computational Mathematics 2025W
Lernergebnisse
Kompetenzen
(*)Students are acquainted with basic principles concerning stochastic differential equations (SDEs) as well as with fundamental techniques for proving and computing in in this context as required for advanced courses.
Fertigkeiten Kenntnisse
(*)
  • Comprehend the construction and properties of the Riemann-Stieltjes-Integral;
  • Know the path properties of the Wiener process and independently prove elementary properties;
  • Understand the construction of the Ito integral;
  • Understand the properties if the Ito integral and prove them indepndently in simple situations;
  • Know and apply Ito's lemma;
  • Comprehend the construction of stochastic differential equations and understand the proof of existence and uniqueness;
  • Know standard examples of solutions of stochastic differential equations, e.g., the geometrical Brownian motion and the Ornstein-Uhlenbeck process;
  • Apply transformation methods for stochastic differential equations, e.g., Lamperti's transform and Girsanov's theorem;
  • Know the construction of the Stratonovich integral and its relationship to the Ito integral;
  • Comprehend the definition of Markov and diffusion processes and apply them to stochastic differential equations;
  • Understand the relationship between stochastic differential equations and partial differential equations, in particular determine Kolmogorov's forward and backward equations or the Fokker-Planck equation, respectively, from the coefficients of a stochastic differential equation.
(*)Riemann-Stieltjes integral, Construction and properties of the Ito integral, Ito's Lemma, stochastic differential equations, geometric Brownsian motion and Ornstein-Uhlenbeck process, transformation methods for SDEs, Girsanov's theorem, Stratonovich integral, Markov- and Diffusion processes, Kolmogorov's forward and backward equation, Fokker-Planck equation, connection to partial differential equations
Beurteilungskriterien (*)Written exam
Lehrmethoden (*)Blackboard presentation
Abhaltungssprache Englisch
Literatur (*)
  • Bernt Oksendal, Stochastic Differential Equations, Springer Verlag
  • Tomas Björk, Arbitrage Theory in Continuous Time, Cambridge University Press
Lehrinhalte wechselnd? Nein
Sonstige Informationen (*)Knowledge from probability theory and the theory of stochastic processes is necessary.
Äquivalenzen (*)402STMESDEV22: VL Stochastic Differential Equations (3 ECTS) + 201MASEPTMS22: SE Probability theory and mathematical statistics (1.5 ECTS)
Gilt als absolviert, wenn (*)402STMESDEV22: VO Stochastic Differential Equations (3 ECTS) + 403PTMSSDEV22: VL Stochastic Differential Equations 2 (3 ECTS)
Präsenzlehrveranstaltung
Teilungsziffer -
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