International audienceWe prove the Malliavin regularity of the solution of a stochastic differential equation driven by a fractional Brownian motion of Hurst parameter H > 0:5. The result is based on the Fréchet differentiability with respect to the input function for deterministic differential equations driven by Hölder continuous functions. It is also shown that the law of the solution has a density with respect to the Lebesgue measure, under a suitable nondegeneracy conditio
We study a renewal risk model in which the surplus process of the insurance company is modeled by a compound fractional Poisson process. We establish the long-range dependence property of this non-stationary process. Some results for the ruin probabilities are presented in various assumptions on the distribution of the claim sizes.AMS 2000 subject classifications: Primary 60G22, 60G55, 91B30; secondary 60K05, 33E12.
We establish Talagrand's T1 and T2 inequalities for the law of the solution of a stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H > 1/2. We use the L 2 metric and the uniform metric on the path space of continuous functions on [0, T ]. These results are applied to study small-time and large-time asymptotics for the solutions of such equations by means of a Hoeffding-type inequality.
We study a renewal risk model in which the surplus process of the insurance company is modeled by a compound fractional Poisson process. We establish the long-range dependence property of this non-stationary process. Some results for the ruin probabilities are presented in various assumptions on the distribution of the claim sizes.AMS 2000 subject classifications: Primary 60G22, 60G55, 91B30; secondary 60K05, 33E12.
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