On the Local Time Process of a Skew Brownian Motion

Standard

On the Local Time Process of a Skew Brownian Motion. / Borodin, Andrei Nikolaevich; Salminen, Paavo.

In: Transactions of the American Mathematical Society, Vol. 372, No. 5, 01.09.2019, p. 3597-3618.

Research output: Contribution to journal › Article › peer-review

Harvard

Borodin, AN & Salminen, P 2019, 'On the Local Time Process of a Skew Brownian Motion', Transactions of the American Mathematical Society, vol. 372, no. 5, pp. 3597-3618. https://doi.org/10.1090/tran/7852

APA

Borodin, A. N., & Salminen, P. (2019). On the Local Time Process of a Skew Brownian Motion. Transactions of the American Mathematical Society, 372(5), 3597-3618. https://doi.org/10.1090/tran/7852

Vancouver

Borodin AN, Salminen P. On the Local Time Process of a Skew Brownian Motion. Transactions of the American Mathematical Society. 2019 Sep 1;372(5):3597-3618. https://doi.org/10.1090/tran/7852

Author

Borodin, Andrei Nikolaevich ; Salminen, Paavo. / On the Local Time Process of a Skew Brownian Motion. In: Transactions of the American Mathematical Society. 2019 ; Vol. 372, No. 5. pp. 3597-3618.

BibTeX

@article{f82866928d204aa780e1377c62867249,

title = "On the Local Time Process of a Skew Brownian Motion",

abstract = "We derive a Ray–Knight type theorem for the local time process (in the space variable) of a skew Brownian motion up to an independent exponential time. It is known that the local time seen as a density of the occupation measure and taken with respect to the Lebesgue measure has a discontinuity at the skew point (in our case at zero), but the local time taken with respect to the speed measure is continuous. In this paper we discuss this discrepancy by characterizing the dynamics of the local time process in both of these cases. The Ray–Knight type theorem is applied to study integral functionals of the local time process of the skew Brownian motion. In particular, we determine the distribution of the maximum of the local time process up to a fixed time, which can be seen as the main new result of the paper.",

keywords = "Bessel function, Brownian motion, Inversion formula for Laplace transforms, Local time",

author = "Borodin, {Andrei Nikolaevich} and Paavo Salminen",

note = "Publisher Copyright: {\textcopyright} 2019 American Mathematical Society.",

year = "2019",

month = sep,

day = "1",

doi = "10.1090/tran/7852",

language = "English",

volume = "372",

pages = "3597--3618",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "5",

}

RIS

TY - JOUR

T1 - On the Local Time Process of a Skew Brownian Motion

AU - Borodin, Andrei Nikolaevich

AU - Salminen, Paavo

PY - 2019/9/1

Y1 - 2019/9/1

N2 - We derive a Ray–Knight type theorem for the local time process (in the space variable) of a skew Brownian motion up to an independent exponential time. It is known that the local time seen as a density of the occupation measure and taken with respect to the Lebesgue measure has a discontinuity at the skew point (in our case at zero), but the local time taken with respect to the speed measure is continuous. In this paper we discuss this discrepancy by characterizing the dynamics of the local time process in both of these cases. The Ray–Knight type theorem is applied to study integral functionals of the local time process of the skew Brownian motion. In particular, we determine the distribution of the maximum of the local time process up to a fixed time, which can be seen as the main new result of the paper.

AB - We derive a Ray–Knight type theorem for the local time process (in the space variable) of a skew Brownian motion up to an independent exponential time. It is known that the local time seen as a density of the occupation measure and taken with respect to the Lebesgue measure has a discontinuity at the skew point (in our case at zero), but the local time taken with respect to the speed measure is continuous. In this paper we discuss this discrepancy by characterizing the dynamics of the local time process in both of these cases. The Ray–Knight type theorem is applied to study integral functionals of the local time process of the skew Brownian motion. In particular, we determine the distribution of the maximum of the local time process up to a fixed time, which can be seen as the main new result of the paper.

KW - Bessel function

KW - Brownian motion

KW - Inversion formula for Laplace transforms

KW - Local time

UR - http://www.scopus.com/inward/record.url?scp=85075135392&partnerID=8YFLogxK

U2 - 10.1090/tran/7852

DO - 10.1090/tran/7852

M3 - Article

VL - 372

SP - 3597

EP - 3618

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 5

ER -

ID: 46296238