A0474
Title: A Closed-Form Transition Density Expansion for Elliptic and Hypo-Elliptic SDEs
Authors: Yuga Iguchi - Lancaster University (United Kingdom) [presenting]
Alexandros Beskos - University College London (United Kingdom)
Abstract: We introduce a closed-form expansion for the transition density of elliptic and hypo-ellipticmultivariate Stochastic Differential Equations (SDEs). Our methodology provides approximations of the transition density,easily evaluated via any software that performs symbolic calculations. A major part of thepaper is devoted to an analytical control of the remainder in our expansion for fixed observation step-size.The obtained error bounds validate theoretically the methodology, by characterising the size ofthe distance from the true value. It is the first time that such a closed-form expansion becomesavailable for the important class of hypo-elliptic SDEs, to the best of our knowledge. For ellipticSDEs, closed-form expansions are available, with some works identifying the size of the error forfixed , as per our contribution. Our methodology allows for a uniform treatment of ellipticand hypo-elliptic SDEs, when earlier works are intrinsically restricted to an elliptic setting.We show numerical applications highlighting the effectiveness of our method, by carrying outparameter inference for hypo-elliptic SDEs that do not satisfy stated conditions. The latter aresufficient for controlling the remainder terms, but the closed-form expansion itself is applicablein general settings.
