Nonparametric estimation of trend for SDEs with delay driven by a fractional brownian motion with small noise

2021 ◽  
pp. 1-11
Author(s):  
B. L. S. Prakasa Rao
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Nonparametric Estimation ◽  
Small Noise

Nonparametric estimation of trend for stochastic differential equations driven by sub-fractional Brownian motion

2020 ◽  
Vol 28 (2) ◽  
pp. 113-122
Author(s):  
B. L. S. Prakasa Rao
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Nonparametric Estimation ◽  
Small Noise ◽  
Trend Coefficient

AbstractWe discuss nonparametric estimation of a trend coefficient in models governed by a stochastic differential equation driven by a sub-fractional Brownian motion with small noise.

scholarly journals A Wavelet-Based Almost-Sure Uniform Approximation of Fractional Brownian Motion with a Parallel Algorithm

2014 ◽  
Vol 51 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Dawei Hong ◽  
Shushuang Man ◽  
Jean-Camille Birget ◽  
Desmond S. Lun
Keyword(s):  
Brownian Motion ◽  
Convergence Rate ◽  
Fractional Brownian Motion ◽  
Parallel Algorithm ◽  
Uniform Approximation ◽  
Haar Wavelets ◽  
Hurst Index ◽  
Sample Paths ◽  
Vanishing Moment ◽  
Uniform Expansion

We construct a wavelet-based almost-sure uniform approximation of fractional Brownian motion (FBM) (Bt(H))_t∈[0,1] of Hurst index H ∈ (0, 1). Our results show that, by Haar wavelets which merely have one vanishing moment, an almost-sure uniform expansion of FBM for H ∈ (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an FBM efficiently.

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