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Probabilitats --- Estadística matemàtica --- Estadística --- Anàlisi d'error (Matemàtica) --- Anàlisi de regressió --- Anàlisi de sèries temporals --- Anàlisi de variància --- Anàlisi multivariable --- Anàlisi seqüencial --- Astronomia estadística --- Correlació (Estadística) --- Dependència (Estadística) --- Estadística no paramètrica --- Estadística robusta --- Física estadística --- Mètode dels moments (Estadística) --- Models lineals (Estadística) --- Models no lineals (Estadística) --- Teoria de l'estimació --- Teoria de la predicció --- Tests d'hipòtesi (Estadística) --- Biometria --- Mostreig (Estadística) --- Estadística descriptiva --- Inferència estadística --- Matemàtica estadística --- Mètodes estadístics --- Combinatòria (Matemàtica) --- Lògica --- Lògica matemàtica --- Descomposició (Matemàtica) --- Distribució (Teoria de la probabilitat) --- Fiabilitat (Enginyeria) --- Funcions característiques --- Geometria estocàstica --- Incertesa (Teoria de la informació) --- Integrals de camí --- Jocs d'atzar (Matemàtica) --- Mitjana (Estadística) --- Probabilitats combinatòries --- Processos estocàstics --- Sort --- Teoremes de límit (Teoria de probabilitats) --- Teoria matemàtica de la comunicació --- Variables aleatòries --- Atzar --- Risc (Economia) --- Teoria ergòdica --- Càlcul de probabilitats --- Probabilitat --- Distribution (Probability theory) --- Statistics. --- Stochastic processes. --- Random processes --- Probabilities --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Distribution functions --- Frequency distribution --- Characteristic functions

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This textbook explores two distinct stochastic processes that evolve at random: weakly stationary processes and discrete parameter Markov processes. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study. After recapping the essentials from Fourier analysis, the book begins with an introduction to the spectral representation of a stationary process. Topics in ergodic theory follow, including Birkhoff’s Ergodic Theorem and an introduction to dynamical systems. From here, the Markov property is assumed and the theory of discrete parameter Markov processes is explored on a general state space. Chapters cover a variety of topics, including birth–death chains, hitting probabilities and absorption, the representation of Markov processes as iterates of random maps, and large deviation theory for Markov processes. A chapter on geometric rates of convergence to equilibrium includes a splitting condition that captures the recurrence structure of certain iterated maps in a novel way. A selection of special topics concludes the book, including applications of large deviation theory, the FKG inequalities, coupling methods, and the Kalman filter. Featuring many short chapters and a modular design, this textbook offers an in-depth study of stationary and discrete-time Markov processes. Students and instructors alike will appreciate the accessible, example-driven approach and engaging exercises throughout. A single, graduate-level course in probability is assumed.

Stochastic processes. --- Markov processes. --- Distribution (Probability theory). --- Probabilities. --- Stochastic Processes. --- Markov Process. --- Distribution Theory. --- Probability Theory. --- Processos estocàstics --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- Random processes --- Càlcul estocàstic --- Funcions aleatòries --- Processos aleatoris --- Probabilitats --- Anàlisi estocàstica --- Aproximació estocàstica --- Camps aleatoris --- Filtre de Kalman --- Fluctuacions (Física) --- Martingales (Matemàtica) --- Mètode de Montecarlo --- Processos de Markov --- Processos de ramificació --- Processos gaussians --- Processos puntuals --- Rutes aleatòries (Matemàtica) --- Semimartingales (Matemàtica) --- Sistemes estocàstics --- Teoremes de límit (Teoria de probabilitats) --- Teoria de cues --- Teoria de l'estimació --- Teoria de la predicció --- Distribution (Probability theory)