Existence of solution for stochastic differential equations driven by G-Lévy process with discontinuous coefficients

• Published in: Advances in difference equations Vol. 2017; no. 1; pp. 1 - 13
• Main Authors: Wang, Bingjun, Yuan, Mingxia
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 30.06.2017; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Brownian motion; Coefficients; Difference and Functional Equations; Differential equations; discontinuous coefficients; Economic models; Functional Analysis; G-Lévy process; Mathematical analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Probability theory; stochastic differential equations; upper and lower solution; 60H10; upper and lower solution; 60H20; discontinuous coefficients; Lévy process; stochastic differential equations; 60H05
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-017-1242-y

The existence theory for the vector-valued stochastic differential equations driven by G -Brownian motion and pure jump G -Lévy process ( G -SDEs) of the type d Y t = f ( t , Y t ) d t + g j , k ( t , Y t ) d 〈 B j , B k 〉 t + σ i ( t , Y t ) d B t i + ∫ R 0 d K ( t , Y t , z ) L ( d t , d z ) , t ∈ [ 0 , T ] , with first two and last discontinuous coefficients, is established. It is shown that the G -SDEs have more than one solution if the coefficients f , g , K are discontinuous functions. The upper and lower solution method is used.