One dimensional BSDEs with logarithmic growth application to PDEs

被引：10

作者：

Bahlali, Khaled ^{[1
]}

Kebiri, Omar ^{[2
]}

Khelfallah, Nabil ^{[3
]}

Moussaoui, Hadjer ^{[1
]}

机构：

[1] UTLN, UFR Sci, EA 2134, IMATH, La Garde, France

[2] Univ Abou Bekr Belkaid Tlemcen, Lab Stat & Random Modeling, Tilimsen, Algeria

[3] Univ Mohamed Khider, Lab Appl Math, Biskra, Algeria

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2017年 / 89卷 / 6-7期

关键词：

Backward stochastic differential equations; viscosity solution; semilinear PDEs; logarithmic growth; logarithmic nonlinearity; STOCHASTIC DIFFERENTIAL-EQUATIONS; UNIQUENESS; EXISTENCE; HOMOGENIZATION; STABILITY;

D O I：

10.1080/17442508.2017.1311900

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the existence and uniqueness of solutions to one dimensional BSDEs with generator allowing a logarithmic growth (vertical bar y parallel to ln vertical bar y parallel to + vertical bar z vertical bar root vertical bar ln vertical bar z parallel to) in the state variables y and z. This is done with an Lp - integrable terminal value, for some p > 2. As byproduct, we obtain the existence of viscosity solutions to PDEs with logarithmic nonlinearities.

引用

页码：1061 / 1081

页数：21

共 50 条

[1] One-Dimensional BSDEs with Jumps and Logarithmic Growth
Bouhadjar, El Mountasar Billah
Khelfallah, Nabil
Eddahbi, Mhamed
[J]. AXIOMS, 2024, 13 (06)
[2] ONE-DIMENSIONAL REFLECTED BSDES WITH TWO BARRIERS UNDER LOGARITHMIC GROWTH AND APPLICATIONS
El Asri, Brahim
Oufdil, Khalid
Ourkiya, Nacer
[J]. PROBABILITY AND MATHEMATICAL STATISTICS-POLAND, 2022, 42 (02): : 251 - 282
[3] Stochastic optimal control and BSDEs with logarithmic growth
Bahlali, Khaled
El Asri, Brahim
[J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2012, 136 (06): : 617 - 637
[4] Multidimensional BSDEs with super-linear growth coefficient: Application to degenerate systems of semilinear PDEs
Bahian, K.
Essaky, E.
Hassani, M.
[J]. COMPTES RENDUS MATHEMATIQUE, 2010, 348 (11-12) : 677 - 682
[5] One kind of multiple dimensional Markovian BSDEs with stochastic linear growth generators
Rui Mu
Zhen Wu
[J]. Advances in Difference Equations, 2015
[6] The Lp Cauchy sequence for one-dimensional BSDEs with linear growth generators
Izumi, Yuki
[J]. STATISTICS & PROBABILITY LETTERS, 2013, 83 (06) : 1588 - 1594
[7] One kind of multiple dimensional Markovian BSDEs with stochastic linear growth generators
Mu, Rui
Wu, Zhen
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2015,
[8] Reflected BSDEs with logarithmic growth and applications in mixed stochastic control problems
El Asri, Brahim
Oufdil, Khalid
[J]. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2023, 95 (01) : 23 - 53
[9] EXISTENCE AND UNIQUENESS OF MULTIDIMENSIONAL BSDEs AND OF SYSTEMS OF DEGENERATE PDEs WITH SUPERLINEAR GROWTH GENERATOR
Bahlali, K.
Essaky, E.
Hassani, M.
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2015, 47 (06) : 4251 - 4288
[10] Existence of solutions to one-dimensional BSDEs with semi-linear growth and general growth generators
Fan, ShengJun
[J]. STATISTICS & PROBABILITY LETTERS, 2016, 109 : 7 - 15

← 1 2 3 4 5 →