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One-dimensional diffusion and stochastic differential equation

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  • He, Ping
  • Shen, Yuncong
  • Sun, Wenjie

Abstract

In this paper, we study the condition for a one-dimensional diffusion to satisfy a stochastic differential equation. In the case of regular diffusion, we give a sufficient and nearly necessary condition using scale function and speed measure. For general diffusions, we decompose the state space into regular and shunt pieces, and give a condition for X satisfying a stochastic differential equation on any shunt pieces.

Suggested Citation

  • He, Ping & Shen, Yuncong & Sun, Wenjie, 2022. "One-dimensional diffusion and stochastic differential equation," Statistics & Probability Letters, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:stapro:v:183:y:2022:i:c:s0167715221002844
    DOI: 10.1016/j.spl.2021.109333
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    References listed on IDEAS

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    1. Shen, Yuncong & Ying, Jiangang, 2018. "Excessive measures for linear diffusions," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 132-139.
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