This is a preview. Log in through your library . Abstract We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the ...

A critical branching process {Zk, k = 0, 1, 2,...} in a random environment is considered. A conditional functional limit theorem for the properly scaled process {log Zpu, 0 ≤ u < ∞} is established ...

Explain why probability is important to statistics and data science. See the relationship between conditional and independent events in a statistical experiment. Calculate the expectation and variance ...

CATALOG DESCRIPTION: Advanced topics in random processes: point processes, Wiener processes; Markov processes, spectral representation, series expansion of random processes, linear filtering, Wiener ...

Stochastic differential equations (SDEs) and random processes form a central framework for modelling systems influenced by inherent uncertainties. These mathematical constructs are used to rigorously ...