Functionals on transient stochastic processes with independent increments

K. Urbanik

Displaying similar documents to “Functionals on transient stochastic processes with independent increments”

Stability of stochastic processes defined by integral functionals

K. Urbanik (1992)

Studia Mathematica

Similarity:

The paper is devoted to the study of integral functionals $ʃ_{0}^{\infty} f (X (t, ω)) d t$ for continuous nonincreasing functions f and nonnegative stochastic processes X(t,ω) with stationary and independent increments. In particular, a concept of stability defined in terms of the functionals $ʃ_{0}^{\infty} f (a X (t, ω)) d t$ with a ∈ (0,∞) is discussed.

A characterization of probability measures by f-moments

K. Urbanik (1996)

Studia Mathematica

Similarity:

Given a real-valued continuous function ƒ on the half-line [0,∞) we denote by P*(ƒ) the set of all probability measures μ on [0,∞) with finite ƒ-moments $ʃ_{0}^{\infty} ƒ (x) μ^{* n} (d x)$ (n = 1,2...). A function ƒ is said to have the identification propertyif probability measures from P*(ƒ) are uniquely determined by their ƒ-moments. A function ƒ is said to be a Bernstein function if it is infinitely differentiable on the open half-line (0,∞) and ${(- 1)}^{n} ƒ^{(n + 1)} (x)$ is completely monotone for some nonnegative integer n. The purpose...

Moments of some random functionals

K. Urbanik (1997)

Colloquium Mathematicum

Similarity:

The paper deals with nonnegative stochastic processes X(t,ω)(t ≤ 0) not identically zero with stationary and independent increments right-continuous sample functions and fulfilling the initial condition X(0,ω)=0. The main aim is to study the moments of the random functionals $\int_{0}^{\infty} f (X (τ, ω)) d τ$ for a wide class of functions f. In particular a characterization of deterministic processes in terms of the exponential moments of these functionals is established.

On the moments of sums of independent identically distributed random variables.

Túri, József (2006)

Mathematica Pannonica

Similarity:

A central limit theorem for stochastic processes with independent increments

M. Fisz (1959)

Studia Mathematica

Similarity:

An asymptotic expansion for the distribution of the supremum of a random walk

M. Sgibnev (2000)

Studia Mathematica

Similarity:

Let $S_{n}$ be a random walk drifting to -∞. We obtain an asymptotic expansion for the distribution of the supremum of $S_{n}$ which takes into account the influence of the roots of the equation $1 - \int_{ℝ} e^{s x} F (d x) = 0, F$ being the underlying distribution. An estimate, of considerable generality, is given for the remainder term by means of submultiplicative weight functions. A similar problem for the stationary distribution of an oscillating random walk is also considered. The proofs rely on two general theorems for Laplace...

Renewal theory in $r$ dimensions (I)

A. J. Stam (1969)

Compositio Mathematica

Similarity:

Transition probability density function of a certain diffusion process concentrated on a half line

A Milian (1991)

Applicationes Mathematicae

Similarity:

On the density of some Wiener functionals: an application of Malliavin calculus.

Antoni Sintes Blanc (1992)

Publicacions Matemàtiques

Similarity:

Using a representation as an infinite linear combination of chi-square independent random variables, it is shown that some Wiener functionals, appearing in empirical characteristic process asymptotic theory, have densities which are tempered in the properly infinite case and exponentially decaying in the finite case.