Large deviation principle for stochastic differential equations driven by stochastic integrals

開催日時
2024/05/17 金 15:30 - 17:00
場所
3号館552号室
講演者
高野凌史
講演者所属
大阪大学
概要

In this talk, we will focus on the large deviation principle (LDP) for stochastic differential equations driven by stochastic integrals in one dimension. The result can be proved with a minimal use of rough path theory, and this implies the LDP for many class of rough volatility models, and it characterizes the asymptotic behavior of implied volatility. First, we introduce a new concept called $\alpha$-Uniformly Exponentially Tightness, and prove the LDP for stochastic integrals on Hölder spaces. Second, we apply this type of LDP to deduce the LDP for stochastic differential equations driven by stochastic integrals in one dimension.