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One Dimensional Stochastic Differential Equations with No Strong Solution

78 citations0/0 files storedJournal of the London Mathematical Society

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Stochastic processes and statistical mechanics

Abstract

Examples are given of continuous functions σ: R→R, with O < δ σ <(x) < K, for which the stochastic differential equation dXt = σ (Xt) dBt has no strong solution.

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2001Stochastic differential equations for Dirichlet processes 2006Weak existence and uniqueness for forward–backward SDEs 2011On Weak Solutions of Stochastic Differential Equations 1984One-dimensional stochastic differential equations involving a singular increasing process 2005One-Dimensional Stochastic Differential Equations with Singular and Degenerate Coefficients 2004Stochastic differential equations driven by stable processes for which pathwise uniqueness fails 1998Pathwise uniqueness and approximation of solutions of stochastic differential equations 2014A stochastic differential equation with a sticky point

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