Examples of renormalized SDEs: SPDERF 2016: Stochastic Partial Differential Equations and Related Fields

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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.
Original languageEnglish
Title of host publicationInternational Conference on Stochastic Partial Differential Equations and Related Fields
PublisherSpringer, Cham
Number of pages15
ISBN (Electronic)978-3-319-74929-7
ISBN (Print)978-3-319-74928-0
DOIs
Publication statusPublished - 3 Jul 2018

Publication series

Name Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 229)

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