Index
additive functional of random walk, 178,
284
adjoint operator, 314
aperiodic random walk, 134
Arzel´ a-Ascoli theorem, 311
Bessel identity, 299
Bessel-Clifford function of the second kind,
297
beta function, 307
Borel-Cantelli lemma, 82
extended Borel-Cantelli lemma, 82
Brownian motion, 25
Cameron-Martin formula, 127
Chapman-Kolmogorov equation, 172
Chung’s law of the iterated logarithm, 132
compound Poisson process, 292
convolution, 28, 300, 301
Cram´ er’s large deviation principle, 6
critical dimensions, 145
densely defined linear operator, 314
Dirac function, 25, 28
Dirichlet form, 95
Donsker-Varadhan’s large deviations, 128
entropy condition, 310
entropy method, 309
equicontinuity, 311
essential smoothness on
R+,
11
essentially smooth function, 2
exponential moment generating function,
12
exponential Tauberian theorem, 24
exponential tightness, 7
Fenchel-Legendre transform, 2
Feynman-Kac formula, 91, 93
first entry formula, 137
Fourier inversion, 299, 300
Fourier transform, 299, 302
Fourier transformation, 95
Friedrichs’ extension theorem, 94, 315
artner-Ellis theorem on large deviations, 5
Gagliardo-Nirenberg inequality, 77, 86
good rate function, 2
Green’s function, 27, 297
of random walk, 235, 236
partial of random walk, 135
ground state solution, 86, 131
high moment asymptotics, 59, 86
hitting time, 137, 152
i.i.d. sequence, 6
increment functional of random walk, 178
infinitesimal generator, 93, 94
intersection local time, 25
p-multiple self —, 46
of random walks, 177
double self —, 160
mutual —, 26, 27, 36
mutual of random walks, 133, 144,
145, 187
renormalized p-multiple self—, 58, 132
renormalized self —, 48, 53, 111, 161,
177, 257
self —, 26
self of random walk, 133
intersection of independent ranges, 133,
145, 177, 187
isometric linear operator, 299
Kolmogorov’s continuity theorem, 35, 310,
313
evy process, 251
Lagrange multiplier, 305, 307
large deviation principle (LDP), 5
law of the iterated logarithm (LIL), 81, 121
for Brownian motions, 83
Le Gall’s moment identity, 33
local time, 36, 37, 102, 139, 152
logarithmic moment generating function, 1,
24
lower semi-continuity, 2
Markov process, 56
331
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