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Multifractal Fractional Ornstein-Uhlenbeck Processes
- Publication Year :
- 2020
-
Abstract
- The Ornstein-Uhlenbeck process can be seen as a paradigm of a finite-variance and statistically stationary rough random walk. Furthermore, it is defined as the unique solution of a Markovian stochastic dynamics and shares the same local regularity as the one of the Brownian motion. A natural generalization of this process able to reproduce the local regularity of a fractional Brownian motion of parameter H is provided by the fractional Ornstein-Uhlenbeck process. Based on previous works, we propose to include some Multifractal corrections to this picture using a Gaussian Multiplicative Chaos. The aforementioned process, called a Multifractal fractional Ornstein-Uhlenbeck process, is a statistically stationary finite-variance process. Its underlying dynamics is non-Markovian, although non-anticipating and causal. The numerical scheme and theoretical approach are based on a regularization procedure, that gives a meaning to this dynamical evolution, which unique solution converges towards a well-behaved stochastic process.<br />Comment: 21 pages, 3 figures, a reference added
- Subjects :
- Mathematics - Probability
Physics - Fluid Dynamics
60G22, 60H05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2011.09503
- Document Type :
- Working Paper