A new proof on the distribution of the local time of a Wiener process

Miklós Csörgo; Qi Man Shao

doi:10.1016/0167-7152(94)90178-3

A new proof on the distribution of the local time of a Wiener process

Miklós Csörgo^*, Qi Man Shao

^*Corresponding author for this work

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

Abstract

Let W(t) be a standard Wiener process with local time L(x, t). It is well-known that, as stochastic processes, L(0, t) and sup_{o ≤ s ≤ t}W(s) have the same distribution (Lévy, 1939). Here we give a new derivation of the distribution of L(x, t + h) - L(x, t) for each x ∈ R¹, t, h ≥ 0.

Original language	English
Pages (from-to)	285-290
Number of pages	6
Journal	Statistics and Probability Letters
Volume	19
Issue number	4
DOIs	https://doi.org/10.1016/0167-7152(94)90178-3
Publication status	Published - 15 Mar 1994
Externally published	Yes

Keywords

Local time
Wiener process

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10.1016/0167-7152(94)90178-3

Cite this

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title = "A new proof on the distribution of the local time of a Wiener process",

abstract = "Let W(t) be a standard Wiener process with local time L(x, t). It is well-known that, as stochastic processes, L(0, t) and supo ≤ s ≤ tW(s) have the same distribution (L{\'e}vy, 1939). Here we give a new derivation of the distribution of L(x, t + h) - L(x, t) for each x ∈ R1, t, h ≥ 0.",

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author = "Mikl{\'o}s Cs{\"o}rgo and Shao, \{Qi Man\}",

year = "1994",

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T1 - A new proof on the distribution of the local time of a Wiener process

AU - Csörgo, Miklós

AU - Shao, Qi Man

PY - 1994/3/15

Y1 - 1994/3/15

N2 - Let W(t) be a standard Wiener process with local time L(x, t). It is well-known that, as stochastic processes, L(0, t) and supo ≤ s ≤ tW(s) have the same distribution (Lévy, 1939). Here we give a new derivation of the distribution of L(x, t + h) - L(x, t) for each x ∈ R1, t, h ≥ 0.

AB - Let W(t) be a standard Wiener process with local time L(x, t). It is well-known that, as stochastic processes, L(0, t) and supo ≤ s ≤ tW(s) have the same distribution (Lévy, 1939). Here we give a new derivation of the distribution of L(x, t + h) - L(x, t) for each x ∈ R1, t, h ≥ 0.

KW - Local time

KW - Wiener process

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:A1994NB00200005

UR - https://www.scopus.com/pages/publications/43949147584

U2 - 10.1016/0167-7152(94)90178-3

DO - 10.1016/0167-7152(94)90178-3

M3 - Journal Article

SN - 0167-7152

VL - 19

SP - 285

EP - 290

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 4

ER -

A new proof on the distribution of the local time of a Wiener process

Abstract

Keywords

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