MATH3030 Stochastic Calculus I (5 cr)

Cooperation network course

Network: Vaasa Higher Education Consortium

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Network: Cross-institutional studies in advanced courses in mathematics and statistics

This course is offered through the Network for Advanced Studies in Mathematics. These studies are available for the following degree students:

  • Bachelor's Degree Programme in Mathematics
  • Master's Degree Programme in Mathematics
  • Bachelor's Degree Programme in Mathematics (Subject Teacher)
  • Master's Degree Programme in Mathematics (Subject Teacher)
  • Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
  • Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
  • Doctoral Programme in Mathematics and Statistics
  • Doctoral Programme in Mathematics and Science (Specialication in Mathematics)

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Grading scale:
0-5
Language:
English

Description

Stochastic Integration We learn the stochastic integration theory where both integrand and integrator are stochastic processes. We begin with processes of finite variation with jumps and point processes. Calculus with functions of finite variation. Point processes and Poisson process on a Borel space. Mean intensity measure and Palm distribution. Stochastic integrals in L^2, Laplace transform, and change of measure formula. Levy processes from point processes in space-time, Levy-Khinchine formula. Change of probabiliy measure formula. Elements of Malliavin calculus in Poisson space. Creation and annihilation difference operators, anticipative Skorokhod integral and integration by parts formula. Predictability and martingales. The course continues in the following period as Stochastic Calculus 2 (MATH3040), where we will deal with Wiener process, elements of Malliavin calculus in Wiener space, and Ito stochastic calculus w.r.t continuous martingales.

Learning outcomes

Learning outcomes: to empower the students with applicable knowledge of the fundamentals of stochastic calculus and its powerful mathematical tools.

Description of prerequisites

Probability Theory 1 and 2 or equivalent knowledge.