Stochastic B-Series and Order Conditions for Exponential Integrators

  • Alemayehu Adugna Arara
  • Kristian Debrabant
  • Anne KværnøEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


We discuss stochastic differential equations with a stiff linear part and their approximation by stochastic exponential Runge–Kutta integrators. Representing the exact and approximate solutions using B-series and rooted trees, we derive the order conditions for stochastic exponential Runge–Kutta integrators. The resulting general order theory covers both Itô and Stratonovich integration.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alemayehu Adugna Arara
    • 1
  • Kristian Debrabant
    • 2
  • Anne Kværnø
    • 3
    Email author
  1. 1.Hawassa UniversityDepartment of MathematicsHawassaEthiopia
  2. 2.University of Southern DenmarkDepartment of Mathematics and Computer ScienceOdense MDenmark
  3. 3.Norwegian University of Science and Technology - NTNUDepartment of Mathematical SciencesTrondheimNorway

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