Yamada-Watanabe Results for Stochastic Differential Equations with Jumps
By Mátyás Barczy, Zenghu Li, Gyula Pap. 2013
53 citations recorded by the source corpus.
Recently, Kurtz (2007, 2014) obtained a general version of the Yamada-Watanabe and Engelbert theorems relating existence and uniqueness of weak and strong solutions of stochastic equations covering also the case of stochastic differential equations with jumps. Following the original method of Yamada and Watanabe (1971), we give alternative proofs for the following two statements: pathwise uniqueness implies uniqueness in the sense of probability law, and weak existence together with pathwise uniqueness implies strong existence for stochastic differential equations with jumps.
Subfields: Control and Systems Engineering, Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8cf12a852f2fa77038cf1b648f4a3474137e2d75
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Control and Systems Engineering
In Finance
In Mathematical Physics
Citations in the corpus
- Stochastic differential equation with jumps for multi-type continuous state and continuous time branching processes with immigration (2014, background): “134 Barczy et al. for λ ∈ R+ and i ∈ {1, . . . , d}, and ψ(λ) := 〈β,λ〉 − ∫ Ud ( e−〈λ,z〉 − 1 ) ν(dz), λ ∈ R+. Further, the function R+ × R+ 3 (t,λ) 7→ v(t,λ) is continuous. Remark 2.5. This theorem is a special case of Theorem 2.7 of Duffie et al. (2003) with m = d, n = 0 and zero killing rate. The u”
- Jump type stochastic differential equations with non-Lipschitz coefficients: Non-confluence, Feller and strong Feller properties, and exponential ergodicity (2017, background): “Now by Theorem 2 of Barczy et al. (2015), for each n ∈ N, a unique strong solution X to (2.”