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We consider stochastic differential equations driven by some Volterra processes. Under time reversal, these equations are transformed into past dependent stochastic differential equations driven by a standard Brownian motion. We are then in…

Probability · Mathematics 2012-12-24 Laurent Decreusefond

For backward stochastic Volterra integral equations (BSVIEs) in multi-dimensional Euclidean spaces, comparison theorems are established in a systematic way for the adapted solutions and adapted M-solutions. For completeness, comparison…

Probability · Mathematics 2012-08-13 Tianxiao Wang , Jiongmin Yong

We study linear backward stochastic Volterra integral equations (BSVIEs) on the infinite time horizon. By introducing weighted function spaces with exponential decay, we establish existence and uniqueness of adapted M-solutions. We…

Probability · Mathematics 2026-03-17 Samia Yakhlef , Hilel Ardjan

We study Backward Stochastic Differential Equations on a probability space equipped with a Brownian filtration. We assume that the terminal value and the generator at zero are merely integrable. Moreover, the generator is assumed to be…

Probability · Mathematics 2022-08-09 Tomasz Klimsiak , Maurycy Rzymowski

With the terminal value $|\xi|$ admitting some given exponential moment, we put forward and prove several existence and uniqueness results for the unbounded solutions of quadratic backward stochastic differential equations whose generators…

Probability · Mathematics 2024-09-23 Yan Wang , Yaqi Zhang , Shengjun Fan

This paper aims at solving one-dimensional backward stochastic differential equations (BSDEs) under weaker assumptions. We establish general existence, uniqueness, and comparison results for bounded solutions, $L^p (p>1)$ solutions and…

Probability · Mathematics 2015-08-12 ShengJun Fan

In this paper, we deal with a class of multivalued backward doubly stochastic differential equations with time delayed coefficients. Based on a slight extension of the existence and uniqueness of solutions for backward doubly stochastic…

Probability · Mathematics 2013-08-15 Wen Lu , Yong Ren , Lanying Hu

In this paper, we consider the backward stochastic differential equation (BSDE) with generator $f(y)|z|^2,$ where the function $f$ is defined on an open interval $D$ and locally integrable. The existence and uniqueness of bounded solutions…

Probability · Mathematics 2021-03-04 Shiqiu Zheng , Lidong Zhang , Lichao Feng

Let E be a type 2 UMD Banach space, H a Hilbert space and let p be in [1,\infty). Consider the following stochastic delay equation in E: dX(t) = AX(t) + CX_t + b(X(t),X_t)dW_H(t), t>0; X(0) = x_0; X_0 = f_0. Here A : D(A) -> E is the…

Functional Analysis · Mathematics 2010-11-15 Sonja Cox , Mariusz Górajski

An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure…

Probability · Mathematics 2012-12-17 Istvan Gyöngy , Sotirios Sabanis

This paper is devoted to solving a multidimensional backward stochastic differential equation with a general time interval, where the generator is uniformly continuous in $(y,z)$ non-uniformly with respect to $t$. By establishing some…

Probability · Mathematics 2017-05-03 Shengjun Fan , Lishun Xiao , Yanbin Wang

We study the problem of existence and uniqueness of solutions of backward stochastic differential equations with two reflecting irregular barriers, $L^p$ data and generators satisfying weak integrability conditions. We deal with equations…

Probability · Mathematics 2016-11-04 Tomasz Klimsiak

In this paper we are concerned with one-dimensional backward stochastic differential equations (BSDE in short) of the following type: \[Y_t=\xi -\int_{t\wedge \tau}^{\tau}Y_r|Y_r|^q dr-\int_{t\wedge \tau}^{\tau}Z_r dB_r,\qquad t\geq 0,\]…

Probability · Mathematics 2009-09-29 A. Popier

This paper is devoted to solving a real valued backward stochastic differential equation with jumps where the time horizon may be finite or infinite. Under linear growth generator, we prove existence of a minimal solution. Using a…

Probability · Mathematics 2012-10-05 Ahmadou Bamba Sow

This paper is dedicated to the analysis of forward backward stochastic differential equations driven by a L{\'e}vy process. We assume that the generator and the terminal condition are path-dependent and satisfy a local Lipschitz condition.…

Probability · Mathematics 2025-10-03 Hannah Geiss , Céline Labart , Adrien Richou , Alexander Steinicke

We establish Burkholder-Davis-Gundy-type inequalities for stochastic Volterra integrals with a completely monotone convolution kernel, which may exhibit singular behaviour at the origin. When the supremum is taken over a finite interval,…

Probability · Mathematics 2025-04-01 Alexandre Pannier

This paper investigates McKean-Vlasov backward stochastic variational inequalities (BSVIs) whose generator depends on the joint law of the solution. We first establish the existence and uniqueness of the solution under globally Lipschitz…

Optimization and Control · Mathematics 2026-04-03 Qi Liu , Yanbo Chen

We consider an infinite horizon, obliquely reflected backward stochastic differential equation (RBSDE). The main contribution of the present work is that we generalize previous results on infinite horizon reflected BSDEs to the setting…

Probability · Mathematics 2023-09-21 Magnus Perninge

We study the following backward stochastic differential equation on finite time horizon driven by an integer-valued random measure $\mu$ on $\mathbb R_+\times E$, where $E$ is a Lusin space, with compensator $\nu(dt,dx)=dA_t\,\phi_t(dx)$:…

Probability · Mathematics 2015-06-09 Elena Bandini

The present paper is devoted to the well-posedness of a type of multi-dimensional backward stochastic differential equations (BSDEs) with a diagonally quadratic generator. We give a new priori estimate, and prove that the BSDE admits a…

Probability · Mathematics 2024-04-17 Guang Yang