This PhD study focusses on the intersection between stochastic differential equations (SDEs) and switching dynamics, a field only scarcely explored so far. The theoretical questions to be answered include: how to define solutions to SDEs with state dependent switching, when solutions cannot be patched together of segments of positive time duration, what are the stochastic properties of such solutions, how do they relate to real life dynamic systems exposed to Brownian noise and rapid switching. The last question exposes the practical relevance of the suggested study, since such systems appear in great numbers in practical life. Theoretical solutions to mathematical models serve as idealized objects expected to resemble real life behavior. Since infinitely rapid switching never appears in practice, due to e.g. switching delays, one should require the observed behavior to approach the theoretical one, when such imperfections approach zero. Fulfilling the latter requirement brings predictive power to the applied model, which is of paramount importance to any practical application of the theory.
PhD stipends are allocated to individuals who hold a Masters degree. PhD stipends are normally for a period of 3 years. It is a prerequisite for allocation of the stipend that the candidate will be enrolled as a PhD student at the Doctoral School of the Faculty of Engineering and Science, in accordance with the regulations of Ministerial Order No. 18 of January 14, 2008 on the PhD Programme at the Universities. According to the Ministerial Order, the progress of the PhD student shall be assessed every six months. It is a prerequisite for continuation of salary payment that the previous progress is approved at the time of the evaluation.