In this chapter we consider parametric inference based on discrete time observations X0, Xt1,...,Xtn from a d-dimensional stochastic process. In most of the chapter the statistical model for the data will be a diffusion model given by a stochastic differential equation. We shall, however, also consider some examples of non-Markovian models, where we typically assume

I would like to thank a number of people who have accompanied me during the writing of this thesis. First and foremost, my sincere gratitude goes to my supervisors Ludwig Fahrmeir and Gareth Roberts, who enriched my work through their advice, ideas and encouragement. I also thank Leonhard Held for his directions during the first stage of my thesis. My research has financially been supported by the German Research Foundation (DFG), the German Academic Exchange Service (DAAD) and the LMU Mentoring programme, in which Francesca Biagini has been a dedicated mentor to me. I deeply appreciate the careful proof-reading and helpful comments by Michael Höhle. Furthermore, I am grateful to my former and present colleagues for their interest in my research and their friendship, in particular to the members of the Semwiso group, my FRAP collaborators, the advocates of good teaching, my fellow women’s representatives, the Cozi Family and my office mates. My family has been a constant source of support, and I greatly acknowledge their personal way of understanding my work. I owe my heartful gratitude to Florian Fuchs, who has been a strong and close partner during all stages of my thesis and who stayed awake until the last sentence was written.