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A stochastic process, or often random process, is a collection of random variables, representing the evolution of some system of random values over time. This is the probabilistic counterpart to a deterministic process. Instead of describing a process which can only evolve in one way (as in the case, for example, of solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy: even if the initial condition (or starting point) is known, there are several (often infinitely many) directions in which the process may evolve. Elementary Stochastic Processes emphasizes on the theory of stochastic processes in an elementary manner. In first chapter, a new optimization method based on a stochastic process is formulated, and several calculation examples are shown to prove its effectiveness as a method to obtain approximate solution for optimization problems. Second chapter proposes a new deterministic envelope function to define non-stationary stochastic processes modeling seismic ground motion accelerations. In third chapter, we propose a numerical method to estimate the fractal dimension of stationary Gaussian stochastic processes using the random Euler numerical scheme and based on an analytical formulation of the fractal dimension for filtered stochastic signals. Fourth chapter focuses on parameter dependence in stochastic modeling—multivariate distributions. In fifth chapter, a new lifetime class with decreasing failure rate is introduced by compounding truncated binomial distribution with any proper continuous lifetime distribution. The properties of the proposed class are discussed, including a formal proof of its probability density function, distribution function and explicit algebraic formulae for its reliability and failure rate functions. In sixth chapter, we propose a new family of circular distributions, obtained by wrapping discrete skew Laplace distribution. Seventh chapter examines relationships among the gene
ISBN: 9781682501078
ISBN13: 9781682501078
Edição: 1ª Edição - 2016
Número de Páginas: 187
Acabamento: HARDCOVER
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