For Kolmogorov equations associated to finite dimensional stochastic differential equations (SDEs) in high dimension, a numerical method alternative to Monte Carlo simulations is proposed. The structure of the SDE is inspired by stochastic Partial Differential Equations (SPDE) and thus contains an underlying Gaussian process which is the key of the algorithm. A series development of the solution in terms of iterated integrals of the Gaussian process is given, it is proved to converge - also in the infinite dimensional limit - and it is numerically tested in a number of examples.

A numerical approach to Kolmogorov equation in high dimension based on Gaussian analysis

Flandoli, Franco;Luo, Dejun;Ricci, Cristiano
2021

Abstract

For Kolmogorov equations associated to finite dimensional stochastic differential equations (SDEs) in high dimension, a numerical method alternative to Monte Carlo simulations is proposed. The structure of the SDE is inspired by stochastic Partial Differential Equations (SPDE) and thus contains an underlying Gaussian process which is the key of the algorithm. A series development of the solution in terms of iterated integrals of the Gaussian process is given, it is proved to converge - also in the infinite dimensional limit - and it is numerically tested in a number of examples.
2021
Settore MAT/06 - Probabilita' e Statistica Matematica
Gaussian process; Iteration schema; Kolmogorov equation; Numerical solution;
File in questo prodotto:
File Dimensione Formato  
1-s2.0-S0022247X20306673-main.pdf

accesso aperto

Tipologia: Published version
Licenza: Creative Commons
Dimensione 1.79 MB
Formato Adobe PDF
1.79 MB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/95180
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 6
social impact