Back to Search
Start Over
Well-posedness and order preservation for neutral type stochastic differential equations of infinite delay with jumps.
- Source :
- AIMS Mathematics (2473-6988); 2024, Vol. 9 Issue 5, p11537-11559, 23p
- Publication Year :
- 2024
-
Abstract
- In this work, we are concerned with the order preservation problem for multidimensional neutral type stochastic differential equations of infinite delay with jumps under non-Lipschitz conditions. By using a truncated Euler-Maruyama scheme and adopting an approximation argument, we have developed the well-posedness of solutions for a class of stochastic functional differential equations which allow the length of memory to be infinite, and the coefficients to be non-Lipschitz and even unbounded. Moreover, we have extended some existing conclusions on order preservation for stochastic systems to a more general case. A pair of examples have been constructed to demonstrate that the order preservation need not hold whenever the diffusion term contains a delay term, although the jump-diffusion coefficient could contain a delay term. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 9
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- AIMS Mathematics (2473-6988)
- Publication Type :
- Academic Journal
- Accession number :
- 177055268
- Full Text :
- https://doi.org/10.3934/math.2024566