Purba Das - Roughness along Schauder type basis
| Dates: | 11 October 2023 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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Purba Das (King's College London) will speak in the Probability seminar. (in-person)
We present several constructions of paths and processes with finite quadratic/ p-th variation along a refining sequence of partitions, extending previous constructions to the non-uniform case. We show that the variation index of a process along a given partition sequence (the infimum value p such that the p-th variation is finite) may not be equal to the reciprocal of Hölder exponent, and provide a pathwise estimator of Hölder exponent. Moreover, we construct a non-Gaussian family of stochastic processes which are statistically indistinguishable from (fractional) Brownian motions. Therefore, when observing a sample path from a process, one should not measure its Hölder roughness by computing p-th variation and should not conclude that the sample is from Brownian motion or fractional Brownian motion even though it exhibits the same properties of those Gaussian processes.
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Max Newman Room G.107
Alan Turing Building
Manchester
