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From almost sure local regularity to almost sure Hausdorff dimension for Gaussian fields
Gaussian processes Hausdorff dimension (multi)fractional Brownian motion multiparameter processes Holder regularity stationarity
2012/6/19
Fine regularity of stochastic processes is usually measured in a local way by local H\"older exponents and in a global way by fractal dimensions. Following a previous work of Adler, we connect these t...
Regularity of Schramm-Loewner Evolutions, annular crossings, and rough path theory
Schramm-Loewner Evolutions annular crossings rough path theory
2011/9/14
Abstract: When studying stochastic processes, it is often fruitful to have an understanding of several different notions of regularity. One such notion is the optimal H\"older exponent obtainable unde...
Path properties and regularity of affine processes on general state spaces
affine processes path properties regularity Markov semimartingales
2011/8/30
Abstract: We provide a new proof for regularity of affine processes on general state spaces by methods from the theory of Markovian semimartingales. On the way to this result we also show that the def...
We review some recent results for a class of fluid mechanics equations called active scalars, with fractional dissipation. Our main examples are the surface quasi-geostrophic equation, the Burgers equ...