Description
Taylor & Francis Ltd Introduction To Stochastic Processes 2006 Edition by Gregory F. Lawler
Emphasizing fundamental mathematical ideas rather than proofs, Introduction to Stochastic Processes, Second Edition provides quick access to important foundations of probability theory applicable to problems in many fields. Assuming that you have a reasonable level of computer literacy, the ability to write simple programs, and the access to software for linear algebra computations, the author approaches the problems and theorems with a focus on stochastic processes evolving with time, rather than a particular emphasis on measure theory.For those lacking in exposure to linear differential and difference equations, the author begins with a brief introduction to these concepts. He proceeds to discuss Markov chains, optimal stopping, martingales, and Brownian motion. The book concludes with a chapter on stochastic integration. The author supplies many basic, general examples and provides exercises at the end of each chapter.New to the Second Edition:Expanded chapter on stochastic integration that introduces modern mathematical financeIntroduction of Girsanov transformation and the Feynman-Kac formulaExpanded discussion of Ito's formula and the Black-Scholes formula for pricing optionsNew topics such as Doob's maximal inequality and a discussion on self similarity in the chapter on Brownian motionApplicable to the fields of mathematics, statistics, and engineering as well as computer science, economics, business, biological science, psychology, and engineering, this concise introduction is an excellent resource both for students and professionals. Preface to Second EditionPreface to First EditionPRELIMINARIESIntroductionLinear Differential EquationsLinear Difference EquationsExercisesFINITE MARKOV CHAINSDefinitions and ExamplesLarge-Time Behavior and Invariant ProbabilityClassification of StatesReturn TimesTransient StatesExamplesExercisesCOUNTABLE MARKOV CHAINSIntroductionRecurrence and TransiencePositive Recurrence and Null RecurrenceBranching ProcessExercisesCONTINUOUS-TIME MARKOV CHAINSPoisson ProcessFinite State SpaceBirth-and-Death ProcessesGeneral CaseExercisesOPTIMAL STOPPINGOptimal Stopping of Markov ChainsOptimal Stopping with CostOptimal Stopping with DiscountingExercisesMARTINGALESConditional ExpectationDefinition and ExamplesOptional Sampling TheoremUniform IntegrabilityMartingale Convergence TheoremMaximal InequalitiesExercisesRENEWAL PROCESSESIntroductionRenewal EquationDiscrete Renewal ProcessesM/G/1 and G/M/1 QueuesExercisesREVERSIBLE MARKOV CHAINSReversible ProcessesConvergence to EquilibriumMarkov Chain AlgorithmsA Criterion for RecurrenceExercisesBROWNIAN MOTIONIntroductionMarkov PropertyZero Set of Brownian MotionBrownian Motion in Several DimensionsRecurrence and TransienceFractal Nature of Brownian MotionScaling Rules Brownian Motion with Drift ExercisesSTOCHASTIC INTEGRATIONIntegration with Respect to Random WalkIntegration with Respect to Brownian MotionIto's Formula Extensions if Ito's FormulaContinuous MartingalesGirsanov TransformationFeynman-Kac FormulaBlack-Scholes FormulaSimulationExercisesSuggestions for Further ReadingIndex