Construction of analytical solutions to systems of two stochastic differential equations

Construction of analytical solutions to systems of two stochastic differential equations

A scheme for the stochastization of systems of ordinary differential equations (ODEs) based on Itô calculus is presented in this article. Using the presented techniques, a system of stochastic differential equations (SDEs) can be constructed in such a way that eliminating the stochastic component yi...

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Published in:Open mathematics (Warsaw, Poland) Vol. 21; no. 1; pp. 108133 - 336
Main Authors: Navickas, Zenonas, Telksniene, Inga, Telksnys, Tadas, Marcinkevicius, Romas, Ragulskis, Minvydas
Format: Journal Article
Language:English
Published: Warsaw De Gruyter 11-11-2023
De Gruyter Poland
Subjects:
35R60
60H10
Differential calculus
differential equation
Differential equations
Exact solutions
Itô equation
Numerical integration
stochastic calculus
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Abstract A scheme for the stochastization of systems of ordinary differential equations (ODEs) based on Itô calculus is presented in this article. Using the presented techniques, a system of stochastic differential equations (SDEs) can be constructed in such a way that eliminating the stochastic component yields the original system of ODEs. One of the main benefits of this scheme is the ability to construct analytical solutions to SDEs with the use of special vector-valued functions, which significantly differs from the randomization approach, which can only be applied via numerical integration. Moreover, using the presented techniques, a system of ODEs and SDEs can be constructed from a given diffusion function, which governs the uncertainty of a particular process.
AbstractList A scheme for the stochastization of systems of ordinary differential equations (ODEs) based on Itô calculus is presented in this article. Using the presented techniques, a system of stochastic differential equations (SDEs) can be constructed in such a way that eliminating the stochastic component yields the original system of ODEs. One of the main benefits of this scheme is the ability to construct analytical solutions to SDEs with the use of special vector-valued functions, which significantly differs from the randomization approach, which can only be applied via numerical integration. Moreover, using the presented techniques, a system of ODEs and SDEs can be constructed from a given diffusion function, which governs the uncertainty of a particular process.
Author Ragulskis, Minvydas
Marcinkevicius, Romas
Telksnys, Tadas
Telksniene, Inga
Navickas, Zenonas
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  organization: Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania
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SubjectTerms 35R60
60H10
Differential calculus
differential equation
Differential equations
Exact solutions
Itô equation
Numerical integration
stochastic calculus
Title Construction of analytical solutions to systems of two stochastic differential equations
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