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Probability theory and stochastic processes [electronic resource] : worked examples / by Odile Pons.

By: Pons, Odile.
Material type: materialTypeLabelBookPublisher: Singapore : World Scientific, [2020]Description: 1 online resource (ix, 249 p.).ISBN: 9789811213533; 9811213534.Subject(s): Probabilities | Stochastic processesGenre/Form: Electronic books.DDC classification: 519.2 Online resources: Access to full text is restricted to subscribers.
Contents:
Probability measures and spaces -- Probability distributions -- Generating function and discrete distributions -- Laplace transform and characteristic function -- Continuous distributions -- Empirical processes and weak convergence -- Discrete martingales and stopping times -- Time-continuous martingales -- Jump processes -- Continuous processes.
Summary: "The book is intended to undergraduate students, it presents exercices and problems with rigorous solutions covering the mains subject of the course with both theory and applications. The questions are solved using simple mathematical methods: Laplace and Fourier transforms provide direct proofs of the main convergence results for sequences of random variables. The book studies a large range of distribution functions for random variables and processes: Bernoulli, multinomial, exponential, Gamma, Beta, Dirichlet, Poisson, Gaussian, Chi2, ordered variables, survival distributions and processes, Markov chains and processes, Brownian motion and bridge, diffusions, spatial processes"--Publisher's website.
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Mode of access: World Wide Web.

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"The book is intended to undergraduate students, it presents exercices and problems with rigorous solutions covering the mains subject of the course with both theory and applications. The questions are solved using simple mathematical methods: Laplace and Fourier transforms provide direct proofs of the main convergence results for sequences of random variables. The book studies a large range of distribution functions for random variables and processes: Bernoulli, multinomial, exponential, Gamma, Beta, Dirichlet, Poisson, Gaussian, Chi2, ordered variables, survival distributions and processes, Markov chains and processes, Brownian motion and bridge, diffusions, spatial processes"--Publisher's website.

Probability measures and spaces -- Probability distributions -- Generating function and discrete distributions -- Laplace transform and characteristic function -- Continuous distributions -- Empirical processes and weak convergence -- Discrete martingales and stopping times -- Time-continuous martingales -- Jump processes -- Continuous processes.

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