Invariant Measures of Ultimately Bounded Stochastic Processes

Modeling of bounded stochastic processes

Random processes of bounded variation are generated by using of randomized sinusoidal model and nonlinear filter model. In the randomized sinusoidal model, random noises ar\e introduced in phase angles; while in the nonlinear filter model, a set of nonlinear Itô differential equations are employed. In both methods, the spectral density of a modeled random process can be matched by adjusting mod...

INVARIANT MEASURES FOR MARKOV PROCESSES(i)

Existence of Bounded Invariant Measures in Ergodic Theory

Smoothing and occupation measures of stochastic processes

This is a review paper about some problems of statistical inference for one-parameter stochastic processes, mainly based upon the observation of a convolution of the path with a non-random kernel. Most of the results are known and presented without proofs. The tools are first and second order approximation theorems of the occupation measure of the path, by means of functionals defined on the sm...

Vector measures of bounded γ-variation and stochastic integrals

Here, the driving process B is a (semi)martingale (for instance, a Brownian motion), and φ is a stochastic process satisfying suitable measurability and integrability conditions. This observation has been used by various authors as the starting point of a theory of stochastic integration for vector-valued processes. Let X be a Banach space. In [5] we characterized the class of functions φ : (0,...