An extension of bifractional Brownian motion

2010/02/19 by Xavier Bardina, Bardina, Xavier, Khalifa Es-Sebaiy +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1002.3680

openalex publication_date 2010/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce and study a self-similar Gaussian process that is the bifractional Brownian motion B^H,K with parameters H∈ (0,1) and K∈(1,2) such that HK∈(0,1). A remarkable difference between the case K∈(0,1) and our situation is that this process is a semimartingale when 2HK=1.

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