LpSolutions of One-Dimensional Backward Stochastic Differential Equations with Continuous Coefficients

DOI10.1080/07362994.2010.503456zbMath1201.60057OpenAlexW2019089763MaRDI QIDQ4932833

Shaokuan Chen

Publication date: 7 October 2010

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362994.2010.503456

zbMATH Keywords

backward stochastic differential equationsuniformly continuous\(L^p\) solution

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30)

Related Items (15)

Bounded solutions, \(L^p\) \((p > 1)\) solutions and \(L^1\) solutions for one dimensional BSDEs under general assumptions ⋮ \(L^p\) solution of general mean-field BSDEs with continuous coefficients ⋮ L^p (1 < p ⩽ 2) solutions of one-dimensional BSDEs whose generator is weakly monotonic in y and non-Lipschitz in z ⋮ The \(L^p\) Cauchy sequence for one-dimensional BSDEs with linear growth generators ⋮ \(L^p (p > 1)\) solutions of BSDEs with generators satisfying some non-uniform conditions in \(t\) and \(\omega\) ⋮ \(L^p\)-solution for BSDEs driven by a Lévy process ⋮ L^p solutions of general time interval BSDEs with generators satisfying a p-order weak stochastic-monotonicity condition ⋮ One-dimensional BSDEs with left-continuous, lower semi-continuous and linear-growth generators ⋮ \(L^p\) solutions of multidimensional BSDEs with weak monotonicity and general growth generators ⋮ \(L^1\) solutions of non-reflected BSDEs and reflected BSDEs with one and two continuous barriers under general assumptions ⋮ \(L^p\) \((p>1)\) solutions for one-dimensional BSDEs with linear-growth generators ⋮ L^p (p ≥ 1) solutions of multidimensional BSDEs with monotone generators in general time intervals ⋮ Unnamed Item ⋮ Mean-field backward stochastic differential equations driven by G-Brownian motion with uniformly continuous coefficients ⋮ Backward stochastic differential equations driven by \(G\)-Brownian motion with uniformly continuous coefficients in \((y, z)\)

Cites Work

• Unnamed Item
• Adapted solution of a backward stochastic differential equation
• Quadratic BSDEs with convex generators and unbounded terminal conditions
• Some uniqueness results for one-dimensional BSDEs with uniformly continuous coefficients
• Backward stochastic differential equations with continuous coefficient
• Conjugate convex functions in optimal stochastic control
• Multidimensional backward stochastic differential equations with uniformly continuous coeffi\-cients
• BSDEs with polynomial growth generators
• Backward stochastic differential equations and partial differential equations with quadratic growth.
• Adapted solutions of backward stochastic differential equations with non- Lipschitz coefficients
• BSDE with quadratic growth and unbounded terminal value
• \(L^p\) solutions of backward stochastic differential equations.
• Linear Quadratic Optimal Stochastic Control with Random Coefficients
• Backward Stochastic Differential Equations in Finance

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