A Generalized Occupation Time Formula For Continuous Semimartingales

2006/12/22 by Raouf Ghomrasni, Ghomrasni, Raouf
Economics, Econometrics and Finance · Mathematics · #60H05 #60J65 #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.math/0612699

openalex publication_date 2006/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for a wide class of functions F that: lim_{ε\downarrow 0} \frac1ε ∫₀^t \F(s, X_s) - F(s, X_s - ε)\ d_s = - ∫₀^t∫_\R F(s, x) d L_s^x where X_t is a continuous semi-martingale, (L_t^x, x ∈ \R, t ≥ 0) its local time process and (_t, t ≥ 0) its quadratic variation process.

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