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Well-posedness of stochastic Volterra equations with non-Lipschitz coefficients
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Multidimensional Backward Stochastic Differential Equations with Left-Lipschitz Coefficients
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Numerical Integration of Stochastic Differential Equations with Nonglobally Lipschitz Coefficients
SIAM Journal on Numerical Analysis, 2005The paper investigates correct ways of discretization for stochastic differential equations (SDEs) with coefficients that are not bounded, and are only locally but not globally Lipschitz, on a fixed finite time horizon. A class of SDEs is considered with a Lyapunov function, which guarantees non-explosion.
Milstein, G.N., Tretyakov, Michael V.
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Anticipated backward stochastic differential equations with left-Lipschitz coefficient
Statistics & Probability Letters, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiong, Yafang, Xu, Xiaoming
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Backward stochastic differential equations with locally Lipschitz coefficient
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2001The author considers the multi-dimensional backward stochastic differential equation for \(t\in [0,1]\), \[ Y_t=\xi+\int_t^1 f(s,Y_s,Z_s)ds-\int_t^1 Z_sdW_s. \] It is proved that this equation has a unique solution \((Y_t,Z_t)\) if 1) \(f\) is progressively measurable; 2) \(f\) is of sublinear growth: \(|f(t,y,z)|\leq M(1+|y|^\alpha+|z|^\alpha)\); 3) \(
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BSDEs with right upper-semicontinuous reflecting obstacle and stochastic Lipschitz coefficient
Random Operators and Stochastic Equations, 2019Abstract This paper proves the existence and uniqueness of a solution to reflected backward stochastic differential equations with a lower obstacle, which is assumed to be right upper-semicontinuous. The result is established where the coefficient is stochastic Lipschitz by using some tools from the general theory of processes such as ...
Marzougue, Mohamed, El Otmani, Mohamed
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A framework of BSDEs with stochastic Lipschitz coefficients
ESAIM: Probability and Statistics, 2020In this paper, we suggest an effective technique based on random time-change for dealing with a large class of backward stochastic differential equations (BSDEs for short) with stochastic Lipschitz coefficients. By means of random time-change, we show the relation between the BSDEs with stochastic Lipschitz coefficients and the ones with bounded ...
O, Hun, Kim, Mun-Chol, Pak, Chol-Kyu
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Fractional anticipated BSDEs with stochastic Lipschitz coefficients
Random Operators and Stochastic Equations, 2018Abstract In this paper, we deal with an anticipated backward stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H ∈
Sow, Ahmadou Bamba, Diouf, Bassirou Kor
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