Numerical sets

L ²

Space of summable square function

a.s.

Almost surely

E

Mathematical expectation

r.v.

Random variable

r.r.v.

Real random variable

Convergence a.s. of sequence X _n to X

? , ? _{L ²()}

Scalar product in L ²

? ? _{L ²()}

Norm L ²

Var

Variance

Cov

Covariance

?

Min( , )

X ? N( m, ? ²)

Normal law of means m and of variance ? ²

A ^T

Transposed matrix A

Hilbert space generated by , scalar or multivariate processes

Projection on Hilbert space generated by Y _{( t ? K)}

X _T

Stochastic process defined on T (time describes T)

p.o.i.

Process with orthogonal increments

p.o.s.i.

Process with orthogonal and stationary increments

Prediction at instant K knowing the measurements of the process Y _K of instants 1 to K ?1

Prediction error

Filtering at instant K knowing its measurements of instants 1 to K

Filtering error

Gradient of function

The set of element X which verify the property

1 _D

Indicative function of a set D