Wyniki wyszukiwania - BazTech

1

Seminarium z teorii potencjału procesów stochastycznych na Politechnice Wrocławskiej

Byczkowski T., Żak T.

Wiadomości Matematyczne

|

2017

|

T. 53, nr 2

257--290

PL

Niniejszy artykuł, przedstawia dokonania i drogę badawczą grupy Tomasza Byczkowskiego, zajmującą się probabilistyką na przestrzeniach liniowych i grupach.

2

Extremal properties of one-dimensional Cauchy-type measures

Byczkowski T., Żak T.

Probability and Mathematical Statistics

|

2015

|

Vol. 35, Fasc. 2

247--266

EN

In the paper we investigate some extremal properties of intervals for the one-dimensional Cauchy measure, related to isoperimetric inequalities. We also consider the analogous properties for the onedimensional sections of the multidimensional isotropic Cauchy measure. In particular, among intervals with the fixed measure we find the ones with the extremal measure of the boundary. It turns out that, contrary to the Gaussian case, the type of extremal set depends on the value of the measure.

3

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

EN

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.

4

One-dimensional symmetric stable Feynman-Kac semigroups

Byczkowska H., Byczkowski T.

Probability and Mathematical Statistics

|

2001

|

Vol. 21, Fasc. 2

381--404

EN

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.

5

On the Schroedinger operator based on the fractional Laplacian

Bogdan K., Byczkowski T.

Bulletin of the Polish Academy of Sciences. Mathematics

|

2001

|

Vol. 49, no 3

291-301

EN

We announce new results in the potential theory of Schroedinger operators based on the fractional Laplacian on Euclidean spaces of arbitrary dimension. We concentrate on questions related to gaugeability and existence of q-harmonic functions. Results are obtained by analyzing properties of symmetric [alpha]-stable Levy processes on Rd, including the recurrent case. We also provide some explicit examples of gauge functions for a general class of domains.

6

Potential theory of Schrödinger operator based on fractional Laplacian

Bogdan K., Byczkowski T.

Probability and Mathematical Statistics

|

2000

|

Vol. 20, Fasc. 2

293--335

EN

We develop potential theory of Schrödinger operators based on fractional Laplacian on Euclidean spaces of arbitrary dimension. We focus on questions related to gaugeability and existence of q-harmonic functions. Results are obtained by analyzing properties of a symmetric α-stable Lévy process on Rd, including the recurrent case. We provide some relevant techniques and apply them to give explicit examples of gauge functions for a general class of domains.

7

Anzelm Iwanik (1946-1998)

Byczkowski T., Downarowicz T., Lipecki Z., Romanowicz Z.

Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne

|

1999

|

[Z] 35

191-200

8

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

EN

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.