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Multidimensional Backward Stochastic Differential Equations with Left-Lipschitz Coefficients

open access: yesMultidimensional 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, 2005
The 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, 2020
zbMATH 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, 2001
The 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, 2019
Abstract 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, 2020
In 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, 2018
Abstract 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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