2020/04/13 by Antoine Ayache, Ayache, Antoine, Julien Hamonier +1
Economics, Econometrics and Finance · #60G17 #60G22 #60G52 #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2004.05874
openalex publication_date 2020/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main goal of this paper is to construct a wavelet-type random series\nrepresentation for a random field X, defined by a multistable stochastic\nintegral, which generates a multifractional multistable Riemann-Liouville\n(mmRL) process Y. Such a representation provides, among other things, an\nefficient method of simulation of paths of Y. In order to obtain it, we\nexpand in the Haar basis the integrand associated with X and we use some\nfundamental properties of multistable stochastic integrals. Then, thanks to the\nAbel's summation rule and the Doob's maximal inequality for discrete\nsubmartingales, we show that this wavelet-type random series representation of\nX is convergent in a strong sense: almost surely in some spaces of continuous\nfunctions. Also, we determine an estimate of its almost sure rate of\nconvergence in these spaces.\n