Introduction to Probability and Stochastic Processes with Applications

Index

absorbed Brownian motion, 477

absorbing state, 354

aperiodic, 355

aperiodic Markov chain, 355

arbitrage, 500

arbitrage opportunity, 506

arithmetic mean, 317

asset pricing

first fundamental theorem, 508

second fundamental theorem, 508

basic principle of counting, 539

generalization, 540

Bayes estimator, 287

Bayes’ rule, 26, 270

birth-and-death process, 378, 420

Black-Scholes equation, 524

Borel

σ-algebra, see σ-algebra of Borel

subset of , 4

Brownian motion, 473

Lévy’s characterization, 480

standard, 473

Brownian motion reflected at the origin, 477

Brownian motion with drift, 478

canonical filtration, 463

canonical form of the transition matrix, 359

central moment

around the mean, 89

around zero, 88

Chapman-Kolmogorov equations, 350

Chernoff bounds, 334

coefficient of variation, 90

combinations, 543

conditional expectation of a random variable

given a σ-algebra, 282

given an event, 280

contingent claim, 498

European, 506

convergence

almost sure, 322

of random vectors, 329

in L^r, 320

in distribution, 325

of random vectors, 329

in probability, 319

of random vectors, 329

convolution of density functions, 213

correlation coefficient, 234

covariance, 230

covariance stationary process, 343

determinant of a matrix, 549

distribution

t-Student, 225

a posteriori, 31

a priori, 31

Bernoulli, 117

beta, 172

binomial, 96, 117

negative, 133

Cauchy, 175

chi-square, 165

discrete uniform, ...