A Modern Theory of Random Variation: With Applications in Stochastic Calculus, Financial Mathematics, and Feynman Integration

Index

absolute random variable, 185

accuracy potentiality, 183

action mechanical, 353

additive sub-additive, 128

almost certain, 52

almost everywhere

F-almost everywhere, 136

h-almost everywhere, 136

almost sure, 52

almost surely

F-almost surely, 136, 188

anti-derivative, 52

arbitrage, 437

risk-neutral pricing, 445

arbitrage pricing, 445

asset

underlying, 434

asset value

derivative, 436

growth rate, 440

underlying, 436

volatility, 441

associated triple, 98, 103, 116

association, 111, 136

associated triple, 101

in R^T, 116–119

point-cell, 42, 79, 97

point-cell-dimension set, 98

atomic distribution function, 409

basic observable, 184

binary partition, 95, 96, 342, 400

binary Riemann sums

weak convergence, 408

black swan, 482

Black-Scholes equation, 444

Black-Scholes formula, 433, 442

European call option, 435

BM-continuity, 360–366

definition, 365

Borel sets, 37

Borel-Cantelli, 230, 232

first, 253

second, 253

Brownian motion, 50, 381

c-Brownian motion, 305–307

continuous modification, 316

discretization, 327

drift rate, 307

drifting, 382, 397

geometric, 308–314

increments, 50

infinite variation, 51

properties, 305

random walk, 327

standard, 307

step function, 327

transitions, 50

unbounded variation, 393

variance rate, 307

with drift, 307

Burkill integral, 6, 7, 11

Burkill-complete integral, 3, 14

calculus integral, 8

call option

European, 435

Cameron–Martin–Girsanov, 445

Cauchy extension, 73

Cauchy inequality, 211

Cavalieri, 359

cell, 39, 111

cell function, 128

sub-additive,