Abstract
In this chapter, we will discuss how to obtain the flow properties for solutions of stochastic differential equations with jumps. This chapter is needed for the second part of this book and as the final goal is not to give a detailed account of the theory of stochastic differential equations driven by jump processes, we only give the main arguments, referring the reader to any specialized text on the subject. For example, see [2] (Sect. 6.6) or [48].
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Notes
- 1.
A random field is a family of random variables which depend on the various parameters. In this case, it is the time variable \( t\ge 0 \) and \( z\in \mathbb {R}\). As in Definition 3.5.1, one can extend the definition in order to include the cases of random fields.
- 2.
That is, K is a family of random variables indexed by elements of \( \Lambda \).
- 3.
In general, we will use \( \nabla \) to denote the derivatives with respect to the main variables of the function under consideration. \( \partial \) will be used when differentiating with respect to what may be considered as a parameter of the function.
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Kohatsu-Higa, A., Takeuchi, A. (2019). Flows Associated with Stochastic Differential Equations with Jumps. In: Jump SDEs and the Study of Their Densities. Universitext. Springer, Singapore. https://doi.org/10.1007/978-981-32-9741-8_7
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DOI: https://doi.org/10.1007/978-981-32-9741-8_7
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