Glossary

Symbols

$B(S)$,
$C_b(S)$,
$C_{bu}(S)$,
$C_c^\infty(M)$,
$c_0(S)$,
$C_0(S)$,
$\divergence X$,
$\E(X|\F^\prime)$,
$\E(f|Y)$,
$H^2(\R^d)$,
$\P(A|B)$,

A

B

Baker's Transformation,
Bernoulli-Laplace diffusion model,
Bernoulli scheme,
Bernoulli shift,
Bessel potential operator,
Brownian motion,

C

cadlag function,
Cauchy semigroup,
characteristic function,
closed operator,
commutator,
competitor model,
complete manifold,
complete vector field,
conductance,
conservative semigroup,
continuous contraction semigroup,
continuous semigroup,
continued fraction,
contraction semigroup,
convergence in distribution,
core,

D

determining sequence,
diffusion operator,
diffusion semigroup,
Dirac-operator,
Dirichlet-form,
dissipative,
distribution,
doubly stochastic,
drift,
Duhamel formula,
dynamical system,

E

Ehrenfest chain,
entropy,
equicontinuous,
ergodic Markov operator,
ergodic semigroup,
ergodic transformation,
essentially self-adoint,
exact semigroup,
extended Markov property,
extremal point,

F

Feller chain,
Feller operator,
Feller semigroup,
first integral,
flow,
Fourier transform,
fundamental theorem of calculus,

G

$\G$-distribution,
Gauss map,
generator,
geodesic distance,
$G$-invariant,
$G$-measure,

H

Haar measure,
Harris chain,
heat kernel of $\R^d$,
heat kernel of $\TT^d$,
hitting time,
homomorphic dynamical systems,
Hutchinson metric,
hyperbolic,

I

index of an operator,
integrable function,
integral curve,
invariant measure,
invariant measure of a Markov chain,
invariant set,
irreducible semigroup,
isomorphic dynamical systems,
iterated function system, IFS,

J

K

Kallman-Rota inequality,
Killing field,

L

$\l$-system,
Laplace distribution,
Laplace operator on $\R^d$,
Laplace transform,
law of large numbers,
Lévy metric,

M

Markov chain,
Markovian transition function,
Markov operator,
Markov property,
maximal function,
measure preserving mapping,
Minkowski functional,
mixing semigroup,

N

Neumann boundary conditions,
norming sequence,

O

Ornstein-Uhlenbeck semigroup,

P

Pinsker's inequality,
$\pi$-system,
Poincaré inequality,
Poissonization,
Poisson semigroup,
positive semigroup,
pre-compact,
predator-prey model,
pseudo resolvent,

Q

quadratic variation,

R

Radon measure,
rationally independent,
regular conditional probability,
regular graph,
regular measure,
relatively compact,
resolvent equation,
resolvent operator,
resolvent set,
return time,
reverse martingal,
reverse submartingal,
reversible Markov chain,
Riesz potential operator,
rising sun lemma,

S

self-adjoint operator,
semigroup,
sequentially compact,
shift operator of a Markov chain,
spectral gap,
spectrum,
speed measure,
$1/2$-stable,
p-stable,
standard gaussian,
stationary sequence,
stochastic matrix,
stopping time,
strictly positive measure,
strict Markov property,
sublattice,

T

terminal $\s$-algebra,
tight,
transfer operator,
transitive action,

U

ultracontractive semigroup,
undirected graph,
uniformly stochastically continuous,

V

W

Walsh functions,
weak topology,
weak * topology,

X

Y

Z

Last modified: Wed Nov 6 15:27:11 CET 2024