Text Correction
The author wishes to make the following corrections to the original publication [1].
- In Section 1, Paragraphs 5 and 6 should be revised as follows:
“We develop a unified method for integrating SDEs with GWN and PWN” and
“Since the common correlation function of these processes is continuous, so are its eigenfunctions, so that the paths of the input FD models are continuous.”
- 2.
- In Section 2, the first sentence should be removed.
- 3.
- In Section 4, within the proofs of Theorems 1 and 2, “Miner’s theorem” should be replaced with “Mercer’s theorem.”
- 4.
- In Section 4, the last paragraph should be corrected by replacing a comma with a period:
“The above statements imply that continuous functionals of Cd and Bd converge in distribution to corresponding functionals of C and B, e.g., sup0≤t≤1 |Cd(t)| → sup0≤t≤1 |C(t)| and sup0≤t≤1 |Bd(t)| → sup0≤t≤1 |B(t)| in distribution as d → ∞.”
- 5.
- In Section 5, the last sentence should be corrected to:
“The statement of this theorem holds for any zero-mean jumps with symmetric density and .”
- 6.
- In Section 6, the last paragraph should be revised as follows:
“The practical implications are that (i) the distributions of functionals of XC can be approximated by the corresponding functionals of XC,d whose paths result from paths of Cd by using integration algorithms for ordinary differential equations (ODEs), e.g., the MATLAB ode45-function, and (ii) the same integration algorithms can be used to estimate the distributions of functionals of solutions to linear forms of GWN and PWN processes. There is no need for specialized integration algorithms such as in [6,7] to generate approximate paths of XC. The generation of surrogates XC,d of XC whose properties match to any accuracy the properties of this process uses standard integration algorithms for ODEs.”
- 7.
- In Section 7, the last sentence of the first paragraph should be revised to:
“Statistics of their solutions are estimated from paths of the corresponding FD solutions, which can be obtained by employing available integration algorithms for ODEs, e.g., the MATLAB ode45-function.”
- 8.
- In Section 7.3, in the first paragraph following Equation (13), “since” should be capitalized to “Since.”
- 9.
- In Section 7.3, the penultimate paragraph should be corrected by replacing a comma with a period, as follows:
“The plots of Figure 5 are for c = 1, σ = 0.8, τ = 2, integration time step ∆t = 2/1000 and 100,000 independent paths of XB, XB,d, XC and XC,d.”
- 10.
- In Section 7.4, paragraph 4 should be revised to:
“We also note that the stochastic dimension of the current integration methods is given by the number n of the time steps and that n is much larger than the stochastic dimension d of the proposed method. Moreover, we have obtained accurate solutions for low stochastic dimensions, as seen in Figures 1–5.”
The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.
Reference
- Grigoriu, M.D. Unified Numerical Method for Stochastic Differential Equations with Poisson and Gaussian White Noises. Stats 2026, 9, 47. [Google Scholar] [CrossRef] [Scilit]
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