# Perturbed Brownian motions

作者： Mihael Perman; Wendelin Werner 文章 : 英語 Probability theory and related fields, št. 3, Let. 108 (1997), str. 357-383 WorldCat Članek obravnava stohastični proces, ki ga dobimo, če standardno Brownovo gibanje perturbiramo, ko doseže maksimum ali minimum, in sicer tako, da v tistem trenutku dodamo dušenje, ki Brownovo gibanje ali potiska od izhodišča ali proti izhodišču. Najprej je dokazana eksistenca takega procesa, potem pa so obravnavane njegove lastnosti. Nazadnje obravnavamo še lastnosti trajektorij perturbiranega Brownovega gibanja npr. Hausdorffova dimenzija točk mnogoterosti.We study "perturbed Brownian motions", that can be, loosely speaking, describes as follows: they behave exactly as linear Brownian motion except they hit their maximum or minimum where they get an extra "push". We define with no restrictions on the perturbation parameters a process which has this property and show that its law is unique within a certain "natural class" of processes. In the case where both perturbations (at the maximum and at the minimum) are self-repelling, we show that in fact, moer is true: Such a process can almost surely be constructed from Brownian paths by a one-to-one measurable transformation. This generalizes some results of Carmona-Petit-Yor and Davis. We also derive some fine properties of perturbed Brownian motions (Hausdorff dimension of points of monotonicity for example).  再讀一些... (尚未評分) 0 附有評論 - 成爲第一個。 在此出版品中使用下列字詞搜尋其他文章：

## 詳細書目

文件類型 文章 Mihael Perman; Wendelin Werner 查詢更多有關資訊： Mihael Perman Wendelin Werner 0178-8051 438457956 str. 357-383. Mihael Perman, Wendelin Werner.

### 摘要：

Članek obravnava stohastični proces, ki ga dobimo, če standardno Brownovo gibanje perturbiramo, ko doseže maksimum ali minimum, in sicer tako, da v tistem trenutku dodamo dušenje, ki Brownovo gibanje ali potiska od izhodišča ali proti izhodišču. Najprej je dokazana eksistenca takega procesa, potem pa so obravnavane njegove lastnosti. Nazadnje obravnavamo še lastnosti trajektorij perturbiranega Brownovega gibanja npr. Hausdorffova dimenzija točk mnogoterosti.

We study "perturbed Brownian motions", that can be, loosely speaking, describes as follows: they behave exactly as linear Brownian motion except they hit their maximum or minimum where they get an extra "push". We define with no restrictions on the perturbation parameters a process which has this property and show that its law is unique within a certain "natural class" of processes. In the case where both perturbations (at the maximum and at the minimum) are self-repelling, we show that in fact, moer is true: Such a process can almost surely be constructed from Brownian paths by a one-to-one measurable transformation. This generalizes some results of Carmona-Petit-Yor and Davis. We also derive some fine properties of perturbed Brownian motions (Hausdorff dimension of points of monotonicity for example).

## 連結資料

### Primary Entity

<http://www.worldcat.org/oclc/438457956> # Perturbed Brownian motions
a schema:Article, schema:CreativeWork ;
library:oclcnum "438457956" ;
library:placeOfPublication <http://id.loc.gov/vocabulary/countries/gw> ;
schema:author <http://experiment.worldcat.org/entity/work/data/324353302#Person/perman_mihael> ; # Mihael Perman
schema:author <http://experiment.worldcat.org/entity/work/data/324353302#Person/werner_wendelin> ; # Wendelin Werner
schema:datePublished "1997" ;
schema:description "Članek obravnava stohastični proces, ki ga dobimo, če standardno Brownovo gibanje perturbiramo, ko doseže maksimum ali minimum, in sicer tako, da v tistem trenutku dodamo dušenje, ki Brownovo gibanje ali potiska od izhodišča ali proti izhodišču. Najprej je dokazana eksistenca takega procesa, potem pa so obravnavane njegove lastnosti. Nazadnje obravnavamo še lastnosti trajektorij perturbiranega Brownovega gibanja npr. Hausdorffova dimenzija točk mnogoterosti." ;
schema:description "We study "perturbed Brownian motions", that can be, loosely speaking, describes as follows: they behave exactly as linear Brownian motion except they hit their maximum or minimum where they get an extra "push". We define with no restrictions on the perturbation parameters a process which has this property and show that its law is unique within a certain "natural class" of processes. In the case where both perturbations (at the maximum and at the minimum) are self-repelling, we show that in fact, moer is true: Such a process can almost surely be constructed from Brownian paths by a one-to-one measurable transformation. This generalizes some results of Carmona-Petit-Yor and Davis. We also derive some fine properties of perturbed Brownian motions (Hausdorff dimension of points of monotonicity for example)." ;
schema:exampleOfWork <http://worldcat.org/entity/work/id/324353302> ;
schema:inLanguage "en" ;
schema:isPartOf <http://worldcat.org/issn/0178-8051> ;
schema:name "Perturbed Brownian motions" ;
schema:pagination "št. 3, Let. 108 (1997), str. 357-383" ;
schema:productID "438457956" ;
wdrs:describedby <http://www.worldcat.org/title/-/oclc/438457956> ;
.

### Related Entities

<http://experiment.worldcat.org/entity/work/data/324353302#Person/perman_mihael> # Mihael Perman
a schema:Person ;
schema:familyName "Perman" ;
schema:givenName "Mihael" ;
schema:name "Mihael Perman" ;
.

<http://experiment.worldcat.org/entity/work/data/324353302#Person/werner_wendelin> # Wendelin Werner
a schema:Person ;
schema:familyName "Werner" ;
schema:givenName "Wendelin" ;
schema:name "Wendelin Werner" ;
.

<http://worldcat.org/issn/0178-8051>
a schema:Periodical ;
rdfs:label "Probability theory and related fields" ;
schema:description "Berlin ; Heidelberg ; New York ; Tokyo : Springer, 1986-" ;
schema:issn "0178-8051" ;
.

Content-negotiable representations