Estimating stationary characteristic functions of stochastic systems via semidefinite programming

Khem Raj Ghusinga; Andrew Lamperski; Abhyudai Singhl

doi:10.23919/ECC.2018.8550583

Estimating stationary characteristic functions of stochastic systems via semidefinite programming

Khem Raj Ghusinga, Andrew Lamperski, Abhyudai Singhl

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Scopus citations

Abstract

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.
Pages	2720-2725
Number of pages	6
ISBN (Electronic)	9783952426982
DOIs	https://doi.org/10.23919/ECC.2018.8550583
State	Published - Nov 27 2018
Externally published	Yes
Event	16th European Control Conference, ECC 2018 - Limassol, Cyprus Duration: Jun 12 2018 → Jun 15 2018

Publication series

Name	2018 European Control Conference, ECC 2018

Other

Other	16th European Control Conference, ECC 2018
Country/Territory	Cyprus
City	Limassol
Period	6/12/18 → 6/15/18

Bibliographical note

Funding Information:
ACKNOWLEDGMENT AS is supported by the National Science Foundation Grant ECCS-1711548.

Publisher Copyright:
© 2018 European Control Association (EUCA).

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10.23919/ECC.2018.8550583

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Ghusinga, K. R., Lamperski, A., & Singhl, A. (2018). Estimating stationary characteristic functions of stochastic systems via semidefinite programming. In 2018 European Control Conference, ECC 2018 (pp. 2720-2725). Article 8550583 (2018 European Control Conference, ECC 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ECC.2018.8550583

Estimating stationary characteristic functions of stochastic systems via semidefinite programming. / Ghusinga, Khem Raj; Lamperski, Andrew; Singhl, Abhyudai.
2018 European Control Conference, ECC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 2720-2725 8550583 (2018 European Control Conference, ECC 2018).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Ghusinga, KR, Lamperski, A & Singhl, A 2018, Estimating stationary characteristic functions of stochastic systems via semidefinite programming. in 2018 European Control Conference, ECC 2018., 8550583, 2018 European Control Conference, ECC 2018, Institute of Electrical and Electronics Engineers Inc., pp. 2720-2725, 16th European Control Conference, ECC 2018, Limassol, Cyprus, 6/12/18. https://doi.org/10.23919/ECC.2018.8550583

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N2 - 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.

AB - 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.

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Estimating stationary characteristic functions of stochastic systems via semidefinite programming

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