On Stochastic Differential Equations with Jumps of Marcus-Type

07.11.2022, 13:00  –  Campus Golm, House 9, Room 2.22
Forschungsseminar Wahrscheinlichkeitstheorie

Martha Nansubuga (HU Berlin)

We study stochastic differential equations (SDEs) driven by semimartingales with jumps, where the jumps of the solution are obtained as small relaxation time limits of fast curvilinear motions along the solution of a non-linear ordinary differential equation, and between the jumps, the solution to the SDE moves along the (coefficient) vector field in the sense of Marcus [1]. For stochastic integrals driven by a continuous process, stochastic integrals in the Marcus sense coincide with stochastic integrals in the Stratonovich sense and satisfy a chain rule for drivers with jumps. We study SDEs with time-dependent coefficients, which are compared and checked in [2]. I will give an outlook on my ongoing research where such stochastic differential equations are to be applied.

References

[1] Marcus, Steven I, Modeling and approximation of stochastic differential equations driven by semimartingales. Stochastics: An International Journal of Probability and Stochastic Processes 4, no. 3 (1981) pp. 223-245.

[2] Kurtz, Thomas G., Etienne Pardoux, and Philip Protter, Stratonovich stochastic differential equations driven by general semimartingales. In Annales de l’IHP Probabilités et statistiques, vol. 31, no. 2 (1995) pp. 351-377.

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