2016/08/16 by Antoine Ayache, Ayache, Antoine, Julien Hamonier +1
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.48550/arxiv.1608.04752
arxiv created 2016/08/16 · openalex publication_date 2016/08/16 · arxiv updated 2016/08/18 · openalex created_date 2022/08/23 · openalex updated_date 2026/07/28
The study of path behaviour of stochastic processes is a classical topic in probability theory and related areas. In this frame, a natural question one can address is: whether or not sample paths belong to a critical Hölder space? The answer to this question is negative in the case of Brownian motion and many other stochastic processes: it is well-known that despite the fact that Brownian paths satisfy, on each compact interval I, a Hölder condition of any order strictly less than 1/2, they fail to belong to the critical Hölder space C1/2(I). In this article, we show that a different phenomenon happens in the case of linear multifractional stable motion (LMSM): for any given compact interval one can find a critical Hölder space to which sample paths belong. Among other things, this result improves an upper estimate, recently derived in Biermé, Lacaux (2013), on behaviour of LMSM, by showing that the logarithmic factor in it is not needed.