June 2012
Intermediate to advanced
614 pages
11h 48m
English
book
Introduction to Probability and Stochastic Processes with Applications
by Liliana Blanco Castaneda, Viswanathan Arunachalam, Selvamuthu Dharmaraja
Content preview from Introduction to Probability and Stochastic Processes with Applications
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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
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 Lr, 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
negative, 133
Cauchy, 175
chi-square, 165
discrete uniform, ...
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