A Closed-Form Transition Density Expansion for Elliptic and Hypo-Elliptic SDEs

Add to your list(s) Download to your calendar using vCal

• Alexandros Beskos (University College London)
• Monday 11 November 2024, 15:00-16:00
• Seminar Room 2, Newton Institute.

If you have a question about this talk, please contact nobody.

SSD - Stochastic systems for anomalous diffusion

Co-author: Mr Yuga Iguchi   We introduce a closed-form expansion for the transition density of elliptic and hypo-elliptic multivariate Stochastic Differential Equations (SDEs), over a period $\Delta\in (0,1)$, in terms of powers of $\Delta^{k/2}$, $k\ge 0$. Our methodology provides a tractable approximation of the true transition density, which can be easily evaluated via any software that carries out symbolic calculations. A major part of the paper is committed to obtaining analytical results about the size of the residual in our closed-form expansion for fixed $\Delta\in(0,1)$. The produced error bound validates the methodology, by providing a guarantee of increased precision when including extra terms in our proxy and by characterising the size of the distance from the true value.  It is the first time that such a closed-form expansion becomes available for the important class of hypo-elliptic SDEs, to the best of our knowledge. For elliptic SDEs, closed-form expansions are available, with previous works identifying the size of the error for fixed $\Delta$, as per our own contribution. Our methodology follows an approach allowing for a uniform treatment of elliptic and hypo-elliptic SDEs, when earlier works are intrinsically restricted to an elliptic setting.  We show numerical applications that highlight the effectiveness of our method, by carrying out parameter inference for SDE models that do not necessarily satisfy stated conditions. The latter are sufficient for an analytical control of the errors, but the closed-form expansion itself is applicable in general settings.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 2, Newton Institute
• bld31

Note that ex-directory lists are not shown.