Weaves, webs and flows

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F24%3A00597140" target="_blank" >RIV/67985556:_____/24:00597140 - isvavai.cz</a>

Výsledek na webu

<a href="https://projecteuclid.org/journals/electronic-journal-of-probability/volume-29/issue-none/Weaves-webs-and-flows/10.1214/24-EJP1161.full" target="_blank" >https://projecteuclid.org/journals/electronic-journal-of-probability/volume-29/issue-none/Weaves-webs-and-flows/10.1214/24-EJP1161.full</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1214/24-EJP1161" target="_blank" >10.1214/24-EJP1161</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Weaves, webs and flows

Popis výsledku v původním jazyce

We introduce weaves, which are random sets of non-crossing càdlàg paths that cover space-time R × R. The Brownian web is one example of a weave, but a key feature of our work is that we do not assume that the particle motions have any particular distribution. Rather, we present a general theory of the structure, characterization and weak convergence of weaves. We show that the space of weaves has an appealing geometry, involving a partition into equivalence classes under which each equivalence class contains a pair of distinguished objects known as a web and a flow. Webs are natural generalizations of the Brownian web and the flows provide pathwise representations of stochastic flows. Moreover, there is a natural partial order on the space of weaves, characterizing the efficiency with which paths cover space-time, under which webs are precisely minimal weaves and flows are precisely maximal weaves. This structure is key to establishing weak convergence criteria for general weaves, based on weak convergence of finite collections of particle motions.

Název v anglickém jazyce

Weaves, webs and flows

Popis výsledku anglicky

We introduce weaves, which are random sets of non-crossing càdlàg paths that cover space-time R × R. The Brownian web is one example of a weave, but a key feature of our work is that we do not assume that the particle motions have any particular distribution. Rather, we present a general theory of the structure, characterization and weak convergence of weaves. We show that the space of weaves has an appealing geometry, involving a partition into equivalence classes under which each equivalence class contains a pair of distinguished objects known as a web and a flow. Webs are natural generalizations of the Brownian web and the flows provide pathwise representations of stochastic flows. Moreover, there is a natural partial order on the space of weaves, characterizing the efficiency with which paths cover space-time, under which webs are precisely minimal weaves and flows are precisely maximal weaves. This structure is key to establishing weak convergence criteria for general weaves, based on weak convergence of finite collections of particle motions.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA22-12790S" target="_blank" >GA22-12790S: Stochastické systémy v nekonečné dimensi</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Electronic Journal of Probability

ISSN

1083-6489

e-ISSN

1083-6489

Svazek periodika

29

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

82

Strana od-do

1-82

Kód UT WoS článku

001267278400001

EID výsledku v databázi Scopus

2-s2.0-85199786976