Probability and Stochastic Processes

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.
Contents: Probability Measures and SpacesProbability DistributionsGenerating Function and Discrete DistributionsLaplace Transform and Characteristic FunctionContinuous DistributionsEmpirical Processes and Weak ConvergenceDiscrete Martingales and Stopping TimesTime-Continuous MartingalesJump ProcessesContinuous Processes
Readership: Undergraduate students interested in more advanced statistics.Probability;Laplace Transform;Fourier Transform;Weak Convergence;Martingale;Jump Process;Gaussian Process0Key Features:Each section begins with a short summary of the course used in the exercicesThe book contains the basic notions of probability and more advanced results for processesDistribution functions of variables and processes with random parameters having conjugate distributions are studied