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Path-by-path uniqueness of infinite-dimensional stochastic differential equations. (arXiv:1706.07720v1 [math.PR])
来源于:arXiv
Consider the stochastic differential equation $\mathrm dX_t = -A X_t
\,\mathrm dt + f(t, X_t) \,\mathrm dt + \mathrm dB_t$ in a (possibly
infinite-dimensional) separable Hilbert space, where $B$ is a cylindrical
Brownian motion and $f$ is a just measurable, bounded function. If the
components of $f$ decay to 0 in a faster than exponential way we establish
path-by-path uniqueness for mild solutions of this stochastic differential
equation. This extends A. M. Davie's result from $\mathbb R^d$ to Hilbert
space-valued stochastic differential equations. 查看全文>>