Stochastic Calculus for Fractional Brownian Motion and Related Processes. Mishura Y. 2008 (on Springer)

1   4,5  general indicator function
~   8   complex Gaussian measure
^   5   Fourier transform
^_ε   7   e-ball
Z*   41   sup
(f,g)   7   inner product
/f,g/  10   dual operation
|a|   12   a1+...+aN
||I||_p  41   mean norm

B^H   7,9,11   fBm
C^λ   2   set of Holder continuous functions

D   1   domain of the corresponding operator
D^α   3   Riemann–Liouville (or Marchaud) f. derivative

F   5   Fourier transform
F_H   6
f_H(λ)   7   spectral density function

H   12
h   12   Hemite polynomials

I   12   set of all finite multiindeces
I^α   1   Riemann–Liouville fractional integral
I⁰   4   unitary operator
I^α(L)   3   class of {integrated} functions
I_H   16   Wiener integral w.r.t fBm
I_t   41   integral w.r.t fBm

k_H   9

L² _M   13
L^H ₂   16
l   4,5  general indicator function

M^H   10, 119
mesh(A)   8   finite Lebesgue measure

N metric E-capacity

φ_λ(t)   7   characteristic function

r(n)   8   autocovariance function

ρ_I   41   semimetric, generated by the process I

S   5,10   Schwartz space
Ф   11
W   9   Wiener process
ω   <10

fractional Brownian motion  7
long-range dependence  8
self-similar process  7
spectral density function  7
spectral representation  8