 if and only if.
 hence.
 for all
.
 there exists
.

such that.
 set of
such that
takes place.

converges to
.

acts from
to
.

jump of
.
.
 integer part of real number
.
 the number of elements in the set
.
scalar
product of
and
or
with
being mathematical expectation or duality action of
on
.
scalar
product of
and
defined via a summation or integration over the variable
(if there is a possibility of confusion with another variable).
scalar
product in Hilbert space
.
norm
of
in space
.
energy
norm,
for some
.
matrix
with elements
.
closure of set
.
 complex conjugate of number
.
dual
space of space
or adjoint operator of operator
or polar cone to cone
.
 Fourier or Laplace transform of
.
 seminorm consisting of only the highest derivatives, see the section
(
Sobolev spaces
).
.
function
restricted to the interval
.
.
.
 Indicator of event
or indicator function of the set
.
It is equal to 1 if the
is true
(
occurs or
)
and zero otherwise. In particular,
Prob
.

is asymptotically equal to
:
or
for a constant
(in Bayesian analysis context) or random variable
is distributed like
or
is asymptotic expansion of
.
(greater of the two as in "union").
 the minimal
algebra
containing the union of the set collections
and
.
(as in "intersection").
.
.
is the limit

the set of points
where the
is achieved.
indexes
of active constraints at the feasible point
.
affine
hull of the set
.
a.s.  almost surely.
a.e.  almost everywhere.

drift of the process
at time
:
.
 price of a risky bond with zero recovery as observed at
The
is the maturity of the bond.
 ball of radius
centered at
.
volume
of the ball.

(matrix of) volatility of the process
at time
:
.
 Borel field on real line.
 Borel field over the topological space
.
 complement of the set
.
ch.f.  characteristic function.
closure
of
,
see (
Convex Hull, Cone,
Relative Interior
).
convex
hull of
,
see (
Convex hull
).
see the section (
Function spaces
section
).
binomial
coefficients,
,
.
or
 Kronecker's delta.
 boundary of the set
.
subdifferential
of the function
at the point
.
differential
of the function
applied to the argument
.
 in finite element, PDE and Sobolev space sections
"
"
refers to diameter of
(spacial set under consideration).
d.f.  distribution function.
 expectation of
taken with respect to the probability measure
.
 expectation of
applied to the random quantity
.
 risk neutral expectation of
,
see (
Risk neutral pricing
).
 expectation of
with respect to the
forward probability measure, see
(
Tforward probability measure
).
vector
.
 forward price as observed at
with maturity
.
 forward LIBOR observed at
and effective during
,
see (
Forward LIBOR
).
=
,
given the settlement dates structure
.
feasible
direction cone of the set
at the point
.
 characteristic function of a random variable
.
 the
algebra
containing information available at time
.
 the
algebra
generated by the r.v.
.
GMRA  generalized multiresolution analysis.

algebra
containing both (cross product of)
and
.
 Schwartz space (see the formula (
Schwartz
space
)).

chunkiness parameter in finite elements sections, hazard rate in financial
sections.

algebra
generated by credit events or Poisson jumps.
 see the section (
Sobolev spaces
section
).
iff  if and only if.
iid  independent identically distributed.
 interior of set
.
i.o.  infinitely often.
condition
number of matrix
.
 finite difference approximation of the second derivative at the
th
knot of the lattice.
LHS  left hand side (of equation).
see the section (
Function spaces
section
).
 linear operator, usually differential operator of elliptic type or a
generator of Markov process.
 space of linear bounded operators acting from
to
.
strong
operator norm from
to
.
MRA  multiresolution analysis.

geometric drift of the process
at time
:
.
geometric
drift of the process
under numeraire
,
 some martingale.
 normal variable with mean
and standard deviation
.
normal
cone of the set
at the point
.
null
space of matrix or operator
.
positive integers,
.
nonnegative integers,
.
integer
interval,
,
for
.
OST  orthonormal system of translates.
 orthogonal projection on the finite element space
(see the definition (
Orthogonal L2
projection
)).
 price of the riskless bond with zero recovery as observed at
The
is the maturity of the bond.
p.m.  probability measure.
in pr.  in probability. For example,
in pr. means
"
converges to
in probability".
distribution
of the random variable
.
distribution
of the normal variable
.
 probability of the event
.
Prob
 probability of the event
.
 projection of A on B.
the
set of all absolutely continuous measures with respect to the measure
of
in real variable context or the class of "shape functions" in finite element
context.
in finite element context.
set
of permutations of
integers taken from the range
.
set
of permutations of
integers taken from the range
.
RHS  right hand side (of equation).
 Ritz projection on finite element space
(see the definition (
Elliptic Ritz
projection
)).
 riskless rate.
r.v.  random variable.
 real line.

dimensional
space.
nonnegative
quadrant of the
.
.
range
of matrix or operator
.
 correlation of quantities
and
.
 swap rate for a vanilla fixedforfloating LIBOR swap with payments
occurring at
,...,
.
 finite element space.
span
 linear span of the set
.
s.p.m.  subprobability measure.
 support set of the function
.
supp
 support set of the function
.
s.t.  such that.
 stopping time or default time.
tangent
cone of the set
at the point
.
 (column of) geometric volatility of the process
at time
:
.
 sigma algebra generated by path of the process
up
to the time
.
minimal
sigma algebra containing the components
and
.
 spectrum of operator
.
 point spectrum of operator
.
 a value of a derivative at time
.
 (column of) standard Brownian motion at
.
 (column of) standard Brownian motion with respect to the
forward
probability measure.
 (column of) standard Brownian motion with respect to the risk neutral
probability measure.

(column of) standard Brownian motion with respect to the numeraire
.
 see the section (
Sobolev spaces
section
).
 event space (complete description of what may happen).
 spot dollar price of a pound.
dual
space if
is a space with linearity and topology, polar cone if
is a cone, conjugate operator or matrix if
is an operator or a matrix, convex conjugate function if
is a function.
or
 mesh in the chapters on wavelets and finite elements.
or
 scale and transport operations applied to functions
or
(wavelet chapter).
 standard normal variable.
,
spot pound price of a dollar.
 set of all integers,
.
