Results 11 to 20 of about 57,660 (268)
Backward Stochastic Differential Equations on Manifolds [PDF]
Probability Theory and Related Fields, 2004 The problem of finding a martingale on a manifold with a fixed random terminal value can be solved by considering BSDEs with a generator with quadratic growth. We study here a generalization of these equations and we give uniqueness and existence results
Blache, Fabrice
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Anticipated backward stochastic differential equations [PDF]
The Annals of Probability, 2009 In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the ...
Dimbinirina Ramarimbahoaka +2 more
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Semi-linear Degenerate Backward Stochastic Partial Differential Equations and Associated Forward Backward Stochastic Differential Equations [PDF]
Stochastic Processes and their Applications, 2011 In this paper, we consider the Cauchy problem of semi-linear degenerate backward stochastic partial differential equations (BSPDEs in short) under general settings without technical assumptions on the coefficients.
Du, Kai, Zhang, Qi
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Infinite horizon forward–backward stochastic differential equations
Stochastic Processes and their Applications, 2000 Let \(B\) be a standard \(d\)-dimensional Wiener process defined on a probability space \((\Omega ,\mathfrak F,P)\), let \((\mathfrak F_{t})\) be the (augmented) natural filtration of \(B\). An infinite horizon forward-backward stochastic differential equation \[ \begin{aligned} & dX(t) = b(t,X(t),Y(t),Z(t)) dt + \sigma (t,X(t), Y(t),Z(t)) dB(t), \tag ...
Peng, Shige, Shi, Yufeng
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Lp solutions of backward stochastic differential equations
Stochastic Processes and their Applications, 2003 Existence and uniqueness of solutions of the following backward stochastic differential equation are studied: \[ Y_t=\xi +\int _t^Tf(r,Y_r,Z_r)\,\text dr-\int _t^TZ_r\,\text dB_r, \qquad 0\leq t\leq T.\tag{1} \] Here ...
Briand, Ph. +4 more
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Obliquely reflected backward stochastic differential equations [PDF]
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chassagneux, Jean-François +1 more
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Set-valued backward stochastic differential equations
The Annals of Applied Probability, 2023 38 ...
Ararat, Cagin, Ma, Jin, Wu, Wenqian
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Probability, Uncertainty and Quantitative Risk, 2022 For a backward stochastic differential equation (BSDE, for short), when the generator is not progressively measurable, it might not admit adapted solutions, shown by an example. However, for backward stochastic Volterra integral equations (BSVIEs, for short), the generators are allowed to be anticipating.
Wang, Hanxiao +2 more
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Backward Stochastic Differential Equations [PDF]
, 2015 In this chapter, we consider a different type of stochastic differential equation. In the setting of Chapter 17, we specified a solution process X through its dynamics and its initial value, as in ( 17.6). In this chapter, we specify a solution process Y through its dynamics and its terminal value, at a fixed, deterministic time \(T \in ]0,\infty ...
Samuel N. Cohen, Robert J. Elliott
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Analysis of stability for stochastic delay integro-differential equations
Journal of Inequalities and Applications, 2018 In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step ...
Yu Zhang, Longsuo Li
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