Examples of renormalized SDEs

Conference item

Abstract:: We demonstrate two examples of stochastic processes whose lifts to geometric rough paths require a renormalisation procedure to obtain convergence in rough path topologies. Our first example involves a physical Brownian motion subject to a magnetic force which dominates over the friction forces in the small mass limit. Our second example involves a lead-lag process of discretised fractional Brownian motion with Hurst parameter H∈(1/4,1/2), in which the stochastic area captures the quadratic variation of the process. In both examples, a renormalisation of the second iterated integral is needed to ensure convergence of the processes, and we comment on how this procedure mimics negative renormalisation arising in the study of singular SPDEs and regularity structures.

Files:: BCF17.pdf

(Preview, Accepted manuscript, pdf, 187.9KB, Terms of use)

Publisher:: Springer
Host title:: Springer Proceedings in Mathematics and Statistics: SPDERF 2016: Stochastic Partial Differential Equations and Related Fields
Journal:: Springer Proceedings in Mathematics and Statistics: SPDERF 2016: Stochastic Partial Differential Equations and Related Fields More from this journal
Volume:: 229
Pages:: 303-317
Publication date:: 2018-07-03
Acceptance date:: 2017-10-14
DOI:: 10.1007/978-3-319-74929-7_19
ISBN:: 9783319749297

Copyright holder:: Springer International Publishing AG, part of Springer Nature
Notes:: This paper was presented at the International Conference on Stochastic Partial Differential Equations and Related Fields, 10-14 October, 2016 in Bielefeld, Germany. © Springer International Publishing AG, part of Springer Nature 2018. This is the Accepted Manuscript version of the article. The final version is available online from Springer at: https://doi.org/10.1007/978-3-319-74929-7_19

Licence:: Terms and Conditions of Use for Oxford University Research Archive

If you are the owner of this record, you can report an update to it here: Report update to this record