On stochastic processes (I)

On Measurable Stochastic Processes

In recent years probability theory has been formulated mathematically as measure theory; in the case of stochastic processes depending upon a continuous parameter the measures considered are defined on certain subspaces of the space of all functions of a real variable.! This formulation of stochastic processes depending upon a continuous parameter gives rise to certain measurability problems, a...

Notes on stochastic processes

A stochastic process is a type of mathematical object studied in mathematics, particularly in probability theory, which can be used to represent some type of random evolution or change of a system. There are many types of stochastic processes with applications in various fields outside of mathematics, including the physical sciences, social sciences, finance and economics as well as engineering...

Lectures on Stochastic Processes

3 4 CONTENTS 6 Markov chains: stationary distributions 35 6.

On Convergence of Stochastic Processes

where £iX) is the distribution function of the random variable X,f( ) is a real-valued function 5 continuous almost everywhere (p), and the limit is in the sense of the usual weak convergence of distributions. Equation (2) is usually the real center of interest, for many " limit-distribution theorems" are implicit in it. It is clear that for given {pn} and p, the better theorem of this kind wou...

Stochastic Processes