Abstract
A Study of the First-Order Continuous-Time Bilinear Processes Driven by Fractional Brownian Motion
Highlights
Nelson’s diffusion processIn the diffusion process of Nelson (see [4], Chapter 2), the time-varying volatility process may be defined as the second-order solution process (V (t))t≥0 of dV (t) = λ (t) (μ (t) − V (t)) dt + γ (t) V (t) dW(h) (t) in which λ (t) , μ (t) and γ (t) are positive deterministic functions
The continuous-time bilinear (COBL) process has been used to model non linear and/or non Gaussian datasets
In discrete-time series analysis, the assumption of linearity and/or Gaussianity is frequently made. These assumption lead to models that fail to capture certain phenomena commonly observed in practice such as limit cycles, asymmetric distribution, leptokurtosis, etc
Summary
In the diffusion process of Nelson (see [4], Chapter 2), the time-varying volatility process may be defined as the second-order solution process (V (t))t≥0 of dV (t) = λ (t) (μ (t) − V (t)) dt + γ (t) V (t) dW(h) (t) in which λ (t) , μ (t) and γ (t) are positive deterministic functions. This SDE can be obtained from Eq (1). Recently some studies was investigated the existence of such solutions for various families of SDE driven by an fBm
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