Dimension properties of the regularity of jump diffusion processes

Abstract : In this dissertation, we study various dimension properties of the regularity of jump di usion processes, solution of a class of stochastic di erential equations with jumps. In particular, we de- scribe the uctuation of the Hölder regularity of these processes and that of the local dimensions of the associated occupation measure by computing their multifractal spepctra. e Hausdor dimension of the range and the graph of these processes are also calculated.In the last chapter, we use a new notion of “large scale” dimension in order to describe the asymptotics of the sojourn set of a Brownian motion under moving boundaries
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Xiaochuan Yang. Dimension properties of the regularity of jump diffusion processes. General Mathematics [math.GM]. Université Paris-Est, 2016. English. ⟨NNT : 2016PESC1073⟩. ⟨tel-01548358⟩

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