1. Wasserstein distance estimates for jump-diffusion processes.
- Author
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Breton, Jean-Christophe and Privault, Nicolas
- Subjects
- *
STOCHASTIC differential equations , *STOCHASTIC integrals , *JUMP processes , *RANDOM measures , *DISTRIBUTION (Probability theory) - Abstract
We derive Wasserstein distance bounds between the probability distributions of a stochastic integral (Itô) process with jumps (X t) t ∈ [ 0 , T ] and a jump-diffusion process (X t ∗) t ∈ [ 0 , T ] . Our bounds are expressed using the stochastic characteristics of (X t) t ∈ [ 0 , T ] and the jump-diffusion coefficients of (X t ∗) t ∈ [ 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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