Solutions to BSDEs Driven by Multidimensional Fractional Brownian Motions

We study more general backward stochastic differential equations driven by multidimensional fractional Brownian motions. Introducing the concept of the multidimensional fractional (or quasi-) conditional expectation, we study some of its properties. Using the quasi-conditional expectation and multidimensional fractional Itô formula, we obtain the existence and uniqueness of the solutions to BSDEs driven by multidimensional fractional Brownian motions, where a fixed point principle is employed. Finally, solutions to linear fractional backward stochastic differential equations are investigated.

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Reflected Backward Stochastic Differential Equations Driven by Countable Brownian Motions

Journal of Applied Mathematics ◽

10.1155/2013/729636 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 2

Author(s):

Pengju Duan ◽

Min Ren ◽

Shilong Fei

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Point Theorem ◽

Existence And Uniqueness ◽

Backward Stochastic Differential Equations ◽

Brownian Motions ◽

Snell Envelope ◽

New Class

This paper deals with a new class of reflected backward stochastic differential equations driven by countable Brownian motions. The existence and uniqueness of the RBSDEs are obtained via Snell envelope and fixed point theorem.

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SPDIEs and BSDEs Driven by Lévy Processes and Countable Brownian Motions

Journal of Function Spaces ◽

10.1155/2016/5916132 ◽

2016 ◽

Vol 2016 ◽

pp. 1-9

Author(s):

Pengju Duan

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Cauchy Sequence ◽

Existence And Uniqueness ◽

Backward Stochastic Differential Equations ◽

Brownian Motions ◽

New Class ◽

Probabilistic Solution

The paper is devoted to solving a new class of backward stochastic differential equations driven by Lévy process and countable Brownian motions. We prove the existence and uniqueness of the solutions to the backward stochastic differential equations by constructing Cauchy sequence and fixed point theorem. Moreover, we give a probabilistic solution of stochastic partial differential integral equations by means of the solution of backward stochastic differential equations. Finally, we give an example to illustrate.

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Some Results on Backward Stochastic Differential Equations Driven by Fractional Brownian Motions

Stochastic Analysis and Applications to Finance - Interdisciplinary Mathematical Sciences ◽

10.1142/9789814383585_0012 ◽

2012 ◽

pp. 225-242 ◽

Cited By ~ 2

Author(s):

Yaozhong Hu ◽

Daniel Ocone ◽

Jian Song

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Backward Stochastic Differential Equations ◽

Brownian Motions ◽

Fractional Brownian Motions

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Anticipated BSDEs driven by two mutually independent fractional Brownian motions with non-Lipschitz coefficients

Random Operators and Stochastic Equations ◽

10.1515/rose-2020-2051 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Sadibou Aidara ◽

Yaya Sagna

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Existence And Uniqueness ◽

Stochastic Integral ◽

Brownian Motions ◽

Fractional Brownian Motions ◽

Type Integral ◽

Divergence Type ◽

Mutually Independent ◽

Uniqueness Of A Solution

Abstract This paper deals with a class of anticipated backward stochastic differential equations driven by two mutually independent fractional Brownian motions. We essentially establish the existence and uniqueness of a solution in the case of Lipschitz coefficients and non-Lipschitz coefficients. The stochastic integral used throughout the paper is the divergence-type integral.

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Constrained Stochastic Differential Equations Driven by Fractional Brownian Motions: Stationarity and Parameter Estimation Problems

10.21236/ada591767 ◽

2013 ◽

Author(s):

Chihoon Lee

Keyword(s):

Parameter Estimation ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Brownian Motions ◽

Fractional Brownian Motions ◽

Estimation Problems

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DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025706002287 ◽

2006 ◽

Vol 09 (01) ◽

pp. 155-168 ◽

Cited By ~ 6

Author(s):

FULVIA CONFORTOLA

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Hilbert Spaces ◽

Stochastic Partial Differential Equations ◽

Existence And Uniqueness ◽

Backward Stochastic Differential Equations ◽

Uniqueness Result ◽

Infinite Dimensions ◽

Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

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Asymptotic expansions of solutions of stochastic differential equations driven by multivariate fractional Brownian motions having Hurst indices greater than 1/3

Stochastic Analysis and Applications ◽

10.1080/07362994.2018.1483247 ◽

2018 ◽

Vol 36 (6) ◽

pp. 909-931 ◽

Cited By ~ 3

Author(s):

Maksim Vaskouski ◽

Ilya Kachan

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Asymptotic Expansions ◽

Brownian Motions ◽

Fractional Brownian Motions

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Existence and Stability of Solutions of Fuzzy Fractional Stochastic Differential Equations with Fractional Brownian Motions

Advances in Fuzzy Systems ◽

10.1155/2021/3948493 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Elhoussain Arhrrabi ◽

M’hamed Elomari ◽

Said Melliani ◽

Lalla Saadia Chadli

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Exponential Stability ◽

Stochastic Differential Equations ◽

Fractional Brownian Motion ◽

Stability Of Solutions ◽

Brownian Motions ◽

Fractional Brownian Motions ◽

Existence And Stability ◽

Fractional Stochastic Differential Equations

The existence, uniqueness, and stability of solutions to fuzzy fractional stochastic differential equations (FFSDEs) driven by a fractional Brownian motion (fBm) with the Lipschitzian condition are investigated. Finally, we investigate the exponential stability of solutions.

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