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June 5, 2026Infinite Dimensional Analysis Quantum Probability and Related Topics0 citations

Linear Fractional Free Stable Motions and Selfsimilar Free Stable Processes

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MMMakoto MaejimaNSNoriyoshi Sakuma

Key Points

  • This research aims to study linear fractional stable motion and selfsimilar stable processes in the context of free probability.
  • Analyzed the properties of linear fractional stable motion and selfsimilar stable processes.
  • Focused on processes with stationary increments.
  • Utilized concepts from classical and free probability theory.
  • Identified key characteristics of linear fractional stable motion.
  • Established connections between selfsimilar stable processes and free probability.
  • Highlighted the significance of stationary increments in these processes.

Abstract

In classical probability theory, selfsimilar stable processes were well studied in the 1980s. Among others, the so-called linear fractional stable motion is a typical example of selfsimilar stable processes, including the well-known fractional Brownian motion as a special case. In this paper, the linear fractional stable motion and selfsimilar stable processes with stationary increments are studied within the framework of free probability.

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Cite This Study

Maejima et al. (2026) studied this question.

synapsesocial.com/papers/6a2269c9763171746d54853dhttps://doi.org/10.1142/s0219025726500104
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1On Some Stochastic Parabolic Systems Driven by New Fractional Brownian Motions2024
  2. 2Self-similarity and probability density function of the transient response of fractional compound motion2024 · 6 citations
  3. 3Stability Analysis and Numerical Simulations of Fractional Stochastic Systems2026
  4. 4On the pointwise regularity of the Multifractional Brownian Motion and some extensions2024 · 2 citations
  5. 5Large deviation principle for stochastic slow–fast system with nonlinear multiplicative fractional Brownian motion2025