This paper proposes a methodology to estimate characteristic functions of stochastic differential equations that are defined over polynomials. For such systems, the time evolution of the characteristic function is governed by a partial differential equation; consequently, the stationary characteristic function can be obtained by solving an ordinary differential equation (ODE). However, except for a few special cases, the solution to the ODE consists of unknown coefficients. These coefficients are closely related with the stationary moments of the process, which could be estimated by utilizing the fact that the characteristic function is positive definite. The method is illustrated via examples.
|Original language||English (US)|
|Title of host publication||2018 European Control Conference, ECC 2018|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||6|
|State||Published - Nov 27 2018|
|Event||16th European Control Conference, ECC 2018 - Limassol, Cyprus|
Duration: Jun 12 2018 → Jun 15 2018
|Name||2018 European Control Conference, ECC 2018|
|Other||16th European Control Conference, ECC 2018|
|Period||6/12/18 → 6/15/18|
Bibliographical noteFunding Information:
ACKNOWLEDGMENT AS is supported by the National Science Foundation Grant ECCS-1711548.