Continuum Limit of Nearest Neighbor and Random Long-Range Interactions
Tuesday, 12.12.23, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
The thesis deals with the limit behavior of discrete energies with different types of interactions between points. On the one hand, only nearest neighbor interactions are considered and on the other hand random long-range interactions. For the latter some assumptions on the conductance have to be made. In a last step, we will try to combine these two types of interactions and investigate whether some assumptions can be dropped in this case.\n\n \n\n
On strong approximation of SDEs with a discontinuous drift coecient
Tuesday, 19.12.23, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
The classical assumption in the literature on numerical approximation of stochastic differential equations (SDEs) is global Lipschitz continuity of the coecients of the equation.\nHowever, many SDEs arising in applications fail to have globally Lipschitz continuous coecients.\nIn the last decade an intensive study of numerical approximation of SDEs with nonglobally Lipschitz continuous coecients has begun. In particular, strong approximation\nof SDEs with a drift coecient that is discontinuous in space has recently gained a lot of\ninterest. Such SDEs arise e.g. in mathematical finance, insurance and stochastic control\nproblems. Classical techniques of error analysis are not applicable to such SDEs and well\nknown convergence results for standard methods do not carry over in general.\n\nIn this talk I will present recent results on strong approximation of such SDEs.\n\nThe talk is based on joint work with Thomas M¨uller-Gronbach (University of Passau).