On some limit theorems for solutions of stochastic differential equations

Shigetoku Kawabata; Toshio Yamada

Displaying similar documents to “On some limit theorems for solutions of stochastic differential equations”

Euler scheme for solutions of stochastic differential equations with non-Lipschitz coefficients.

Berkaoui, A. (2004)

Portugaliae Mathematica. Nova Série

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Weak averaging of stochastic evolution equations

Ivo Vrkoč (1995)

Mathematica Bohemica

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A theorem on continuous dependence of solutions to stochastic evolution equations on coefficients is established, covering the classical averaging procedure for stochastic parabolic equations with rapidly oscillating both the drift and the diffusion term.

Local and global existence for mild solutions of stochastic differential equations.

Barbu, D. (1998)

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A note on the existence of solutions to some nonlinear functional integral equations.

Purnaras, I.K. (2006)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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An extension of the Yamada-Watanabe condition for pathwise uniqueness to stochastic differential equations with jumps.

Hoepfner, Reinhard (2009)

Electronic Communications in Probability [electronic only]

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Backward stochastic differential equations with stochastic monotone coefficients.

Bahlali, K., Elouaflin, A., N'zi, M. (2004)

Journal of Applied Mathematics and Stochastic Analysis

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$L^{p}$ solutions of BSDEs with stochastic Lipschitz condition.

Wang, Jiajie, Ran, Qikang, Chen, Qihong (2007)

Journal of Applied Mathematics and Stochastic Analysis

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Positivity of the density for the stochastic wave equation in two spatial dimensions

Mireille Chaleyat-Maurel, Marta Sanz-Solé (2003)

ESAIM: Probability and Statistics

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We consider the random vector $u (t, \underset{̲}{x}) = (u (t, x_{1}), \dots, u (t, x_{d}))$ , where $t > 0, x_{1}, \dots, x_{d}$ are distinct points of $ℝ^{2}$ and $u$ denotes the stochastic process solution to a stochastic wave equation driven by a noise white in time and correlated in space. In a recent paper by Millet and Sanz–Solé [10], sufficient conditions are given ensuring existence and smoothness of density for $u (t, \underset{̲}{x})$ . We study here the positivity of such density. Using techniques developped in [1] (see also [9]) based on Analysis on an abstract Wiener space, we characterize...

Discretizing a backward stochastic differential equation.

Zhang, Yinnan, Zheng, Weian (2002)

International Journal of Mathematics and Mathematical Sciences

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