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Pré-Publication, Document De Travail Année : 2022

Wasserstein distance estimates for jump-diffusion processes

Résumé

We derive Wasserstein distance bounds between the probability distributions of a stochastic integral (It\^o) process with jumps $(X_t)_{t\in [0,T]}$ and a jump-diffusion process $(X^\ast_t)_{t\in [0,T]}$. Our bounds are expressed using the stochastic characteristics of $(X_t)_{t\in [0,T]}$ and the jump-diffusion coefficients of $(X^\ast_t)_{t\in [0,T]}$ evaluated in $X_t$, and apply in particular to the case of different jump characteristics. Our approach uses stochastic calculus arguments and $L^p$ integrability results for the flow of stochastic differential equations with jumps, without relying on the Stein equation.

Dates et versions

hal-03894145 , version 1 (12-12-2022)

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Jean-Christophe Breton, Nicolas Privault. Wasserstein distance estimates for jump-diffusion processes. 2022. ⟨hal-03894145⟩
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