CATALOG DESCRIPTION: Fundamentals of random variables; mean-squared estimation; limit theorems and convergence; definition of random processes; autocorrelation and stationarity; Gaussian and Poisson ...

Random walks constitute one of the most fundamental models in the study of stochastic processes, representing systems that evolve in a sequence of random steps. Their applications range from modelling ...

Random walks constitute a foundational concept in probability theory, describing the seemingly erratic movement of particles or agents as they traverse a space in a series of stochastic steps. In many ...

This is a preview. Log in through your library . Abstract We construct a nondecreasing pure jump Markov process, whose jump measure heavily depends on the values taken by the process. We determine the ...

Several economic and financial time series are bounded by an upper and lower finite limit (e.g., interest rates). It is not possible to say that these time series are random walks because random walks ...

Here’s a game Claude Shannon, the founder of information theory, invented in 1948. He was trying to model the English language as a random process. Go to your bookshelf, pick up a random book, open it ...

In the real world, probability is a tough thing to characterize. If I roll a die, what does it mean to say that it has a one-sixth chance of coming up 5? We say that the outcome is random because we ...

Random processes take place all around us. It rains one day but not the next; stocks and bonds gain and lose value; traffic jams coalesce and disappear. Because they’re governed by numerous factors ...

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