Short time kernel asymptotics for rough differential equation driven by\n fractional Brownian motion

2014/03/13 by Yuzuru Inahama, Inahama, Yuzuru · 1 citation
Economics, Econometrics and Finance · Mathematics · #60F99 #60G22 #60H07 #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1403.3181

openalex publication_date 2014/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a stochastic differential equation in the sense of rough path theory\ndriven by fractional Brownian rough path with Hurst parameter H (1/3 < H <=\n1/2) under the ellipticity assumption at the starting point. In such a case,\nthe law of the solution at a fixed time has a kernel, i.e., a density function\nwith respect to Lebesgue measure. In this paper we prove a short time\noff-diagonal asymptotic expansion of the kernel under mild additional\nassumptions. Our main tool is Watanabe's distributional Malliavin calculus.\n

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• Fractional Diffusion Bridges

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