Fully coupled forward-backward stochastic differential equations driven by sub-diffusions

Shuaiqi Zhang; Zhen Qing Chen

doi:10.1016/j.jde.2024.06.003

Fully coupled forward-backward stochastic differential equations driven by sub-diffusions

Shuaiqi Zhang, Zhen Qing Chen^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper, we establish the existence and uniqueness of fully coupled forward-backward stochastic differential equations (FBSDEs in short) driven by anomalous sub-diffusions B_{L_t} under suitable monotonicity conditions on the coefficients. Here B is a Brownian motion on R and L_t:=inf⁡{r>0:S_r>t}, t≥0, is the inverse of a subordinator S with drift κ>0 that is independent of B. Various a priori estimates on the solutions of the FBSDEs are also presented.

Original language	English
Pages (from-to)	337-358
Number of pages	22
Journal	Journal of Differential Equations
Volume	405
DOIs	https://doi.org/10.1016/j.jde.2024.06.003
Publication status	Published - 5 Oct 2024
Externally published	Yes

Keywords

A priori estimate
Anomalous sub-diffusion
Existence and uniqueness
Forward-backward stochastic differential equations

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10.1016/j.jde.2024.06.003

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title = "Fully coupled forward-backward stochastic differential equations driven by sub-diffusions",

abstract = "In this paper, we establish the existence and uniqueness of fully coupled forward-backward stochastic differential equations (FBSDEs in short) driven by anomalous sub-diffusions BLt under suitable monotonicity conditions on the coefficients. Here B is a Brownian motion on R and Lt:=inf⁡\{r>0:Sr>t\}, t≥0, is the inverse of a subordinator S with drift κ>0 that is independent of B. Various a priori estimates on the solutions of the FBSDEs are also presented.",

keywords = "A priori estimate, Anomalous sub-diffusion, Existence and uniqueness, Forward-backward stochastic differential equations",

author = "Shuaiqi Zhang and Chen, \{Zhen Qing\}",

note = "Publisher Copyright: {\textcopyright} 2024 Elsevier Inc.",

year = "2024",

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doi = "10.1016/j.jde.2024.06.003",

language = "English",

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T1 - Fully coupled forward-backward stochastic differential equations driven by sub-diffusions

AU - Zhang, Shuaiqi

AU - Chen, Zhen Qing

PY - 2024/10/5

Y1 - 2024/10/5

N2 - In this paper, we establish the existence and uniqueness of fully coupled forward-backward stochastic differential equations (FBSDEs in short) driven by anomalous sub-diffusions BLt under suitable monotonicity conditions on the coefficients. Here B is a Brownian motion on R and Lt:=inf⁡{r>0:Sr>t}, t≥0, is the inverse of a subordinator S with drift κ>0 that is independent of B. Various a priori estimates on the solutions of the FBSDEs are also presented.

AB - In this paper, we establish the existence and uniqueness of fully coupled forward-backward stochastic differential equations (FBSDEs in short) driven by anomalous sub-diffusions BLt under suitable monotonicity conditions on the coefficients. Here B is a Brownian motion on R and Lt:=inf⁡{r>0:Sr>t}, t≥0, is the inverse of a subordinator S with drift κ>0 that is independent of B. Various a priori estimates on the solutions of the FBSDEs are also presented.

KW - A priori estimate

KW - Anomalous sub-diffusion

KW - Existence and uniqueness

KW - Forward-backward stochastic differential equations

UR - http://www.scopus.com/inward/record.url?scp=85195823819&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2024.06.003

DO - 10.1016/j.jde.2024.06.003

M3 - Article

AN - SCOPUS:85195823819

SN - 0022-0396

VL - 405

SP - 337

EP - 358

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Fully coupled forward-backward stochastic differential equations driven by sub-diffusions

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Keywords

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