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.

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Portugaliae Mathematica. Nova Série

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Weak averaging of stochastic evolution equations

Ivo Vrkoč (1995)

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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.

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Hoepfner, Reinhard (2009)

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Backward stochastic differential equations with stochastic monotone coefficients.

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

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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)

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Backward doubly stochastic differential equations with infinite time horizon

Bo Zhu, Baoyan Han (2012)

Applications of Mathematics

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We give a sufficient condition on the coefficients of a class of infinite horizon backward doubly stochastic differential equations (BDSDES), under which the infinite horizon BDSDES have a unique solution for any given square integrable terminal values. We also show continuous dependence theorem and convergence theorem for this kind of equations.