Index

(χn)n≥0, Haar basis 29

(φn)n≥0, Schauder functions on [0, 1] 29

action functional, 9

albedo, 2

Brownian motion, 28

C([0, T ], Rd), Rd-valued continuous

functions on [0, T ], 49

C∞(R,

0

R), infinitely differntiable real

valued functions on R vanishing at

±∞ 92

Cc

∞(G,

R), real valued infinitely smooth

functions of compact support

contained in an open set G ⊂ R, 70

Ck

(R, R), real valued functions on R with

continuous k-th derivative 92

C0([0, T ],

Rd), Rd-valued

continuous

functions on [0, T ] starting at 0, 51

Cα([0,

1], R), space of α-H¨ older continuous

real valued functions on [0, 1] starting

at 0 28

Cα([0,

0

1], R), separable subspace of real

valued α-H¨ older continuous functions

on [0, 1] starting at 0, 32

Ciesielski isomorphism, 28

c0(N0, R), space of real valued sequences

converging to 0, 32

contraction principle, 40

inverse, 41

dissipativity condition, 53

entropy, 87

exponential tightness, 38

H1([0, T ], R), H1, Cameron–Martin space

of real valued functions on [0, T ], 46

H1([0, T ],

Rd),

H1, Cameron–Martin space

of

Rd-valued

functions on [0, T ], 50

condition (H), 139

hysteresis loopr, 22

interval of resonance, 20

L(R, R; ρdx), real valued functions on R

which are square integrable with

weight ρ 93

L2([0,

T ],

Rd),

Lebesgue measurable

Rd-valued

square integrable functions

on [0, T ] 29

l∞(N0,

R), space of bounded sequences of

real numbers 28

large deviation principle, 37

weak, 38

LDP, see also large deviation principle

· α, α-H¨ older norm 28

· ∞, · , uniform norm 28

Ornstein–Uhlenbeck process, 8

quasipotential, 9

relative entropy, 86

resonant activation, 22

rate function, 37

good, 37

Schilder’s theorem, 50

Schmitt trigger, 22

spectral gap, 111

spectral power amplification coeﬃcient, 13,

modified 129

stochastic resonance, 1

189