The Theory of Stochastic Processes, Volume 10

absorbing barrier absorption autocorrelation function autocovariance function backward equations birth-death process boundary conditions Chapter coefficient consider convergence corresponding defined denote density differential equation diffusion process distribution function eigenvalues equilibrium distribution ergodic Example exponentially distributed finite follows forward equation given Hence increments independent random variables infinite initial condition integral irreducible jump Laplace transform large number limiting linear Markov chain Markov process Markov property matrix mean and variance method normally distributed number of events number of individuals obtain occurs p(xo p₁ parameter particle Po(t Poisson distribution Poisson process probability distribution probability generating function problem process in continuous process X(t queue random walk realization recurrent reflecting barrier renewal process representation result satisfies Section simple random walk small time interval solution spectral stationary process stochastic process Suppose theorem theory transition probabilities uncorrelated values Wiener process