Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion

Interactive comment on “Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion” by Jonathan M. Lilly et al

Review article: Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion

Stochastic process exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm), with the spectral slope at high frequencies being associated with the degree of small-scale roughness or fractal dimension. However, a broad class of real-world signals have a high-frequency slope, like fBm, but a plateau in the vicinity of zero frequency. This...

Interactive comment on “Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion” by Jonathan M. Lilly et al

We would like to thank the reviewer for their very careful reading of the paper. This has helped us to clarify a number of subtle points, and helped us in our goal of balancing a high degree of mathematical rigor with intuitively clear explanations. We appreciate that reviewing a paper as long as this one is a substantial task, and we are very grateful for their effort and patience. We have ans...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory