Index
λ-system, 249
π-system, 249
π λ theorem, 249
absorbing state, 65
active path, 161
adapted stochastic process
continuous time, 30
discrete time, 258
additive spin system, 162
arcsin law, 37, 55
associated measure, 147
Banach space, 250
Bessel process, 130, 220
birth and death chain, 60, 86
Blumenthal zero-one law, 26, 237
Borel-Cantelli lemma, 252
boundary
absorbing, 125
reflecting, 125
sticky, 127, 226
branching chain, 88
Brownian bridge, 8
Brownian motion
conformal invariance, 212
construction, 9
definition, 7
generator in higher dimensions, 231
generator in one dimension, 102
hitting points, 236
older continuity, 11, 17
in higher dimensions, 231
law of the iterated logarithm, 23
evy’s characterization, 211
local time, 214
occupation time, 9, 219
path nondifferentiability, 16
quadratic variation, 18
recurrence and transience, 236
reflection principle, 34
semigroup, 93
tied down, 8
zero set, 33
Burkholder-Davis-Gundy inequalities, 211
c` adl` ag paths, 14
Cauchy process, 101
central limit theorem, 255
Chapman-Kolmogorov equations
continuous time, 58
discrete time, 261
characteristic function, 255
closed operator, 109
compound Poisson process, 15
cone condition, 238
consistent finite-dimensional distributions,
248
contact process, 141, 161
complete convergence theorem, 168, 175
critical value, 163
duality, 162
extinction, 163
graphical representation, 161
strong survival, 165
submodularity, 163
survival, 163
continuous paths, 7
convergence in distribution, 254
core for a generator, 110
coupling
of asymmetric exclusion processes, 188
269
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