Wyniki wyszukiwania - BazTech

1

Transition Density Estimates for Relativistic α-Stable Processes on Metric Spaces

Balsam Hubert, Pietruska-Pałuba Katarzyna

Probability and Mathematical Statistics

|

2020

|

Vol. 40, Fasc. 2

183--204

EN

We prove matching upper and lower bounds for the transition density of relativistic α-stable processes on a d-set (F; p; μ); obtained via subordination. We also identify the corresponding Dirichlet form.

2

On the structure of bounded smooth measures associated with a quasi-regular Dirichlet form

Klimsiak T., Rozkosz A.

Bulletin of the Polish Academy of Sciences. Mathematics

|

2017

|

Vol. 65, no. 1

45--56

EN

We consider a quasi-regular Dirichlet form. We show that a bounded signed measure charges no set of zero capacity associated with the form if and only if the measure can be decomposed into the sum of an integrable function and a bounded linear functional on the domain of the form. The decomposition allows one to describe explicitly the set of bounded measures charging no sets of zero capacity for interesting classes of Dirichlet forms. By way of illustration, some examples are given.

3

Frames and factorization of graph Laplacians

Jorgensen P., Tian F.

Opuscula Mathematica

|

2015

|

Vol. 35, no. 3

293--332

EN

Using functions from electrical networks (graphs with resistors assigned to edges), we prove existence (with explicit formulas) of a canonical Parseval frame in the energy Hilbert space [formula] of a prescribed infinite (or finite) network. Outside degenerate cases, our Parseval frame is not an orthonormal basis. We apply our frame to prove a number of explicit results: With our Parseval frame and related closable operators in [formula] we characterize the Priedrichs extension of the [formula]-graph Laplacian. We consider infinite connected network-graphs G = (V, E), V for vertices, and E for edges. To every conductance function c on the edges E of G, there is an associated pair [formula] where [formula] in an energy Hilbert space, and Δ (=Δc) is the c-graph Laplacian; both depending on the choice of conductance function c. When a conductance function is given, there is a current-induced orientation on the set of edges and an associated natural Parseval frame in [formula] consisting of dipoles. Now Δ is a well-defined semibounded Hermitian operator in both of the Hilbert [formula] and [formula]. It is known to automatically be essentially selfadjoint as an [formula]-operator, but generally not as an [formula] operator. Hence as an [formula] operator it has a Friedrichs extension. In this paper we offer two results for the Priedrichs extension: a characterization and a factorization. The latter is via [formula].

4

Principal eigenvalues for time changed processes of one-dimensional α-stable processes

Shiozawa Y.

Probability and Mathematical Statistics

|

2004

|

Vol. 24, Fasc. 2

355--366

EN

In this paper, we calculate the principal eigenvalues for time changed processes of Brownian motions and symmetric α-stable processes in one dimension.