Wyniki wyszukiwania - BazTech

Ograniczanie wyników

3 Probability and Mathematical Statistics

Znaleziono wyników: 3

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Bessel potentials, Green functions and exponential functionals on half-spaces

Byczkowski T., Ryznar M., Byczkowska H.

Probability and Mathematical Statistics

2006

Vol. 26, Fasc. 1

155--173

The purpose of the paper is to provide precise estimates for the Green function corresponding to the operator (I—Δ)α/2, 0 <α< 2. The potential theory of this operator is based on Bessel potentials Jα=(I—Δ) -α/2. In probabilistic terms it corresponds to a subprobabilistic process obtained from the so-called relativistic a-stable process. We are interested in the theory of the killed process when exiting a fixed half-space. The crucial role in our research is played by (recently found) an explicit form of the Green function of a half-space. We also examine properties of some exponential functionals corresponding to the operator (I—Δ) α/2.

One-dimensional symmetric stable Feynman-Kac semigroups

Byczkowska H., Byczkowski T.

Probability and Mathematical Statistics

2001

Vol. 21, Fasc. 2

381--404

We investigate here one-dimensional Feynman-Kac semigroups based on symmetric α-stable processes. We begin with establishing the properties of Green operators of intervals and halflines on functions from the Kato class. Then we provide a sufficient condition for gaugeability of the halfline(−∞, b) and evaluate the critical value β.

Decomposition of Convolution Semigroups on Groups and the 0-1 Law

Byczkowska H., Byczkowski T.

Probability and Mathematical Statistics

1999

Vol. 19, Fasc. 1

97--104

Let (X(t))t>0, be a stochastically continuous symmetric Lévy process with values in a complete separable group G. We denote by (μt)t>0 the semigroup of one-dimensional distributions of X(t). Suppose that H is a Borel subgroup of G such that μt (H) > 0 for all t > 0. We obtain a decomposition of the generator of the process X ( t ) into a bounded part concentrated on Hc and the generator of a semigroup concentrated on H. This yields the 0-1 law for such processes. We also examine the differentiation of transition probability of the induced Markov process π (X (t)) on the homogeneous space G/H.