Notations
| A⊤ | The transpose of the matrix A |
| A* | The conjugate transpose (Hermitian transpose) of the matrix A |
| ai• | The transpose of the ith row of the matrix A = (aij) |
| B(α, β) | The beta function |
| BH | Fractional Brownian motion with Hurst parameter H |
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Borel σ-algebra on  |
| Cλ([a, b]) | Space of Hölder continuous functions f: [a, b] →
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Riemann–Liouville left-sided fractional derivative of order α |
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Riemann–Liouville right-sided fractional derivative of order α |
| fa+(x) | =(f(x) − f(a+))1(a,b)(x) |
| gb−(x) | =(g(x) − g(b−))1(a,b)(x) |
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Riemann–Liouville left-sided fractional integral of order α |
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Riemann–Liouville right-sided fractional integral of order α |
| Lp([a, b]) | Space of measurable p-integrable functions f : [a, b] →
|
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Space of functions f: [0,T] →
equipped with the norm
|
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The space of Gaussian martingales of the form  , where a ∈  ⊂ L2([0,T]) |
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The set of minimizing functions for the functional f on L2([0, 1]) of the form f(x) = supt∈[0, 1]
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 (0, 1) |
The standard normal distribution |
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The set of natural numbers, i.e. the positive integers |
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The set of real numbers |
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= [0, ∞) |
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The space of measurable functions f: [0,T] → such that |
 | |
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The space of measurable functions f: [0,T] → such that |
 | |
| w[J] | = (wj, i ∈ J), The vector made of the elements of vector w with indices within J. |
| X[·, J] | The submatrix of the matrix X constructed of the columns of the matrix X with indices within the set J; |
| x+ | = max{x, 0} |
| z(t, s) | The Molchan kernel |
| Γ(α) | The gamma function |
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 |
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 where  , ⊂ L2([0, T]) |
(Ω,  , P) |
Complete probability space |
| 1A | Indicator function of a set A |
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Equality in distribution (equality of all finite-dimensional distributions) |
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Convergence in probability |
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