L p Solutions for Multidimensional BDSDEs with Locally Weak Monotonicity Coefficients

Dejian Tian , Runyu Zhu

Chinese Annals of Mathematics, Series B ›› 2021, Vol. 42 ›› Issue (3) : 409 -426.

PDF
Chinese Annals of Mathematics, Series B ›› 2021, Vol. 42 ›› Issue (3) : 409 -426. DOI: 10.1007/s11401-021-0266-5
Article

L p Solutions for Multidimensional BDSDEs with Locally Weak Monotonicity Coefficients

Author information +
History +
PDF

Abstract

In this paper, the authors establish the existence and uniqueness theorem of L p (1 < p ≤ 2) solutions for multidimensional backward doubly stochastic differential equations (BDSDEs for short) under the p-order globally (locally) weak monotonicity conditions. Comparison theorem of L p solutions for one-dimensional BDSDEs is also proved. These conclusions unify and generalize some known results.

Keywords

Backward doubly stochastic differential equation / Locally monotonicity condition / L p solution

Cite this article

Download citation ▾
Dejian Tian, Runyu Zhu. L p Solutions for Multidimensional BDSDEs with Locally Weak Monotonicity Coefficients. Chinese Annals of Mathematics, Series B, 2021, 42(3): 409-426 DOI:10.1007/s11401-021-0266-5

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Bahlali K, Gatt R, Mansouri B, Mtiraoui A. Backward doubly SDEs and SPDEs with superlinear growth generators. Stochastics and Dynamics, 2017, 17: 1-31

[2]

Bally V, Matoussi A. Weak solutions for SPDEs and backward doubly stochastic differential equations. Journal of Theoretical Probability, 2001, 14: 125-164

[3]

Bihari I. A generalization of a lemma of Bellman and its application to uniqueness problem of differential equations. Acta Math. Acad. Sci. Hungar., 1956, 7: 81-94

[4]

Briand P, Delyon B, Hu Y L p solutions of backward stochastic differential equations. Stochastic Process. Appl., 2003, 108: 109-129

[5]

Chen L, Wu Z. A type of general forward-backward stochastic differential equations and applications. Chinese Annals of Mathematics, Series B, 2011, 32: 279-292

[6]

Fan S. L p solutions of multidimensional BSDEs with weak monotonicity and general growth generators. Journal of Mathematical Analysis and Applications, 2015, 432: 156-178

[7]

Hu F, Chen J. Solutions of anticipated backward stochastic differential equations under monotonicity and general increasing conditions. Stochastics: An International Journal of Probability and Stochastic Processes, 2016, 88(2): 267-284

[8]

Kobylanski M. Backward stochastic differential equations and partial equations with quadratic growth. Ann. Probab., 2000, 28: 259-276

[9]

Lepeltier J P, San Martin J. Backward stochastic differential equations with continuous coefficients. Statist. Probab. Lett., 1997, 34: 425-430

[10]

Lin Q. A class of backward doubly stochastic differential equations with non-Lipschitz coefficients. Statistics and Probability Letters, 2009, 79: 2223-2229

[11]

Lin Q, Wu Z. A comparison theorem and uniqueness theorem of backward doubly stochastic differential equations. Acta Mathematicae Applicatae Sinica, English Series, 2011, 27(2): 223-232

[12]

Owo J M. L p solutions of backward doubly stochastic differential equations with stochastic Lipschitz condition and p ∈ (1, 2). ESAIM: Probability and Statistics, 2017, 21: 168-182

[13]

Pardoux E, Peng S. Adapted solution of a backward stochastic differential equation. Systems and Control Letters, 1990, 14: 55-61

[14]

Pardoux E, Peng S. Backward doubly stochastic differential equations and systems of quasilinear SPDEs. Probability Theory and Related Fields, 1994, 98(2): 209-227

[15]

Ren Y, El Otmani M. Generalized reflected BSDEs driven by a Lévy process and an obstacle problem for PDIEs with a nonlinear Neumann boundary condition. Journal of Computational and Applied Mathematics, 2010, 233: 2027-2043

[16]

Shi Y, Gu Y, Liu K. Comparison theorems of backward doubly stochastic differential equations and applications. Stochastic and Analysis and Applications, 2005, 23: 97-110

[17]

Wang F. BSDEs with jumps and path-dependent parabolic integro-differential equations. Chinese Annals of Mathematics, Series B, 2015, 36: 625-644

[18]

Wen J, Shi Y. Backward doubly stochastic differential equations with random coefficients and quasilinear stchastic PDEs. Journal of Mathematical Analysis and Applications, 2019, 476(1): 86-100

[19]

Wu H, Ren R, Hu F. Non-smooth analysis method in optimal investment-BSDE approach. Advances in Difference Equations, 2018, 2018: 460 13 pages

[20]

Wu Z, Zhang F. BDSDEs with locally monotone coefficients and Sobolev solutions for SPDEs. Journal of Differential Equations, 2011, 251: 759-784

[21]

Zhang Q, Zhao H. Stationary solutions of SPDEs and infinite horizon BDSDEs with non-Lipschitz coefficients. Journal of Differential Equations, 2010, 248: 953-991

[22]

Zhu R, Tian D. Existence and uniqueness of solutions for BDSDEs with weak monotonicity coefficients. Statistics and Probability Letters, 2019, 153: 48-55

[23]

Zhu R, Tian D. L p(1 < p < 2) solutions of backward doubly stochastic differential equations with locally monotone coefficients. Communications in Statistics-Theory and Methods, 2021, 50(8): 1856-1872

[24]

Zong Z, Hu F. L p solutions of infinite time interval backward doubly stochastic differential equations under monotonicity and general increasing conditions. Journal of Mathematical Analysis and Applications, 2018, 458: 1486-1511

AI Summary AI Mindmap
PDF

115

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/