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Existence and uniqueness of solution to scalar BSDEs with $L\exp (\mu \sqrt{2\log (1+L)} )$-integrable terminal values: the critical case
- Source :
- Electronic Communications in Probability, Electronic Communications in Probability, 2019, 24, ⟨10.1214/19-ECP254⟩, Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2019, 24, ⟨10.1214/19-ECP254⟩, Electron. Commun. Probab.
- Publication Year :
- 2019
- Publisher :
- HAL CCSD, 2019.
-
Abstract
- In [8], the existence of the solution is proved for a scalar linearly growingbackward stochastic differential equation (BSDE) when the terminal value is$L\exp (\mu \sqrt{2\log (1+L)} )$-integrable for a positive parameter $\mu >\mu _{0}$ with a critical value $\mu _{0}$, and a counterexample is provided to show that the preceding integrability for $\mu \mu _{0}$) is also given in [3] for the preceding BSDE under the uniformly Lipschitz condition of the generator. In this note, we prove that these two results still hold for the critical case: $\mu =\mu _{0}$.
- Subjects :
- Statistics and Probability
$L\exp (\mu \sqrt{2\log (1+L)} )$-integrability
Integrable system
010102 general mathematics
Scalar (mathematics)
backward stochastic differential equation
Lipschitz continuity
Critical value
01 natural sciences
Combinatorics
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
critical case
010104 statistics & probability
Stochastic differential equation
60H10
Uniqueness
0101 mathematics
Statistics, Probability and Uncertainty
existence and uniqueness
Counterexample
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 1083589X
- Database :
- OpenAIRE
- Journal :
- Electronic Communications in Probability, Electronic Communications in Probability, 2019, 24, ⟨10.1214/19-ECP254⟩, Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2019, 24, ⟨10.1214/19-ECP254⟩, Electron. Commun. Probab.
- Accession number :
- edsair.doi.dedup.....3ea2459ba842ea65717e534e71ffa2df