Let X be the solution of the SDE:dX_t=σ(X_t)dB_t+b(X_t)dt,with σ and b ∈C_B~∞(R) such that σ≥λ>0 for some constant λ,and B a real Brownian motion.Let μ be the law of X on E=C([0,1],R)and k ∈E~*-{0},where ...Let X be the solution of the SDE:dX_t=σ(X_t)dB_t+b(X_t)dt,with σ and b ∈C_B~∞(R) such that σ≥λ>0 for some constant λ,and B a real Brownian motion.Let μ be the law of X on E=C([0,1],R)and k ∈E~*-{0},where E~* is the topological dual space of E.Consider the classical form:where u and v are smooth functions on E.We prove that,if is closable for any k in a dense subset of E~* and if the smooth functions are contained in the domain of the generator of the closure of ε_k,σ must be a constant function.展开更多
文摘Let X be the solution of the SDE:dX_t=σ(X_t)dB_t+b(X_t)dt,with σ and b ∈C_B~∞(R) such that σ≥λ>0 for some constant λ,and B a real Brownian motion.Let μ be the law of X on E=C([0,1],R)and k ∈E~*-{0},where E~* is the topological dual space of E.Consider the classical form:where u and v are smooth functions on E.We prove that,if is closable for any k in a dense subset of E~* and if the smooth functions are contained in the domain of the generator of the closure of ε_k,σ must be a constant function.
