TY - JOUR

T1 - Strong solutions of stochastic equations with singular time dependent drift

AU - Krylov, N. V.

AU - Röckner, M.

PY - 2005/2

Y1 - 2005/2

N2 - We prove existence and uniqueness of strong solutions to stochastic equations in domains G ⊂ ℝd with unit diffusion and singular time dependent drift b up to an explosion time. We only assume local L q_Lp-integrability of b in ℝ x G with d/p + 2/q < 1. We also prove strong Feller properties in this case. If b is the gradient in x of a nonnegative function ψ blowing up as G ∋ x → ∂G, we prove that the conditions 2Dtψ ≤ Kψ, 2Dtψ + Δψ ≤ Keεψ, ε ∈ [0, 2), imply that the explosion time is infinite and the distributions of the solution have sub Gaussian tails.

AB - We prove existence and uniqueness of strong solutions to stochastic equations in domains G ⊂ ℝd with unit diffusion and singular time dependent drift b up to an explosion time. We only assume local L q_Lp-integrability of b in ℝ x G with d/p + 2/q < 1. We also prove strong Feller properties in this case. If b is the gradient in x of a nonnegative function ψ blowing up as G ∋ x → ∂G, we prove that the conditions 2Dtψ ≤ Kψ, 2Dtψ + Δψ ≤ Keεψ, ε ∈ [0, 2), imply that the explosion time is infinite and the distributions of the solution have sub Gaussian tails.

KW - Distorted Brownian motion

KW - Singular drift

KW - Strong solutions of stochastic equations

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U2 - 10.1007/s00440-004-0361-z

DO - 10.1007/s00440-004-0361-z

M3 - Article

AN - SCOPUS:12944260508

SN - 0178-8051

VL - 131

SP - 154

EP - 196

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 2

ER -