Some sample function properties of a process with stationary independent increments

Sample path large deviations of a Gaussian process with stationary increments and regularily varying variance

Characterization of unitary processes with independent and stationary increments

This is a continuation of the earlier work [13] to characterize stationary unitary increment Gaussian processes. The earlier assumption of uniform continuity is replaced by weak continuity and with a technical assumption on the domain of the generator, unitary equivalence of the processes to the solution of Hudson-Parthasarathy equation is proved.

Discrete approximation of a stable self-similar stationary increments process

The aim of this paper is to present a result of discrete approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known about the context in which such processes can arise. To our knowledge, discretization and convergence theorems are available only in the case of stable Lévy motions and fra...

Some Properties of Large Excursions of a Stationary Gaussian Process

The present work investigates two properties of level crossings of a stationary Gaussian process X(t) with autocorrelation function RX(τ). We show firstly that if RX(τ) admits finite second and fourth derivatives at the origin, the length of up-excursions above a large negative level −γ is asymptotically exponential as −γ → −∞. Secondly, assuming that RX(τ) admits a finite second derivative at ...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...