ScholarLens Back to search
2021•Stochastic Analysis and ApplicationsRequires access

The first-passage area of Ornstein-Uhlenbeck process revisited

Mario Abundo

Open publisher page 13 citations

Abstract

For Ornstein-Uhlenbeck process X(t), starting from X(0)=x>0, we highlight some results about the first-passage time of X(t) through zero and its first-passage area, that is the random area swept out by X(t), till its first-passage through zero. We study single and joint moments of the first-passage time and first-passage area, and their behaviors, as x→0+ and x→+∞; moreover, we investigate the expected value of the time average of X(t) till the FPT, and the maximum displacement of X(t).

About this research paper

What this paper is about

For Ornstein-Uhlenbeck process X(t), starting from X(0)=x>0, we highlight some results about the first-passage time of X(t) through zero and its first-passage area, that is the random area swept out by X(t), till its first-passage through zero. We study single and joint moments of the first-passage time and first-passage area, and their behaviors, as x→0+ and x→+∞; moreover, we investigate the expected value of the time average of X(t) till the FPT, and the maximum displacement of X(t).

Why it matters

OpenAlex reports 13 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

For Ornstein-Uhlenbeck process X(t), starting from X(0)=x>0, we highlight some results about the first-passage time of X(t) through zero and its first-passage area, that is the random area swept out by X(t), till its first-passage through zero. We study single and joint moments of the first-passage time and first-passage area, and their behaviors, as x→0+ and x→+∞; moreover, we investigate the expected value of the time average of X(t) till the FPT, and the maximum displacement of X(t).

Key concepts: Ornstein–Uhlenbeck process, Mathematics, First-hitting-time model, Zero (linguistics), Stochastic process, Combinatorics, Mathematical analysis, Statistics

Related papers

Related paper 1Related paper 2
Back to paper searchBrowse research topicsOriginal source
The first-passage area of Ornstein-Uhlenbeck process revisited — Research Paper | ScholarLens