Second-order stochastic evolution equations with constant coefficients

Tuesday, October 23, 2012 - 3:15pm - 4:05pm
Keller 3-180
Sergey Lototsky (University of Southern California)
While stochastic parabolicity condition is well-known, there is no
immediate analogue for stochastic equations that are second-order
in time. The objective of this paper is to present a general approach
to the study of well-posedness and stability in Sobolev spaces on $bRd$ of
the initial value problem for second-order in time
stochastic evolution equations with constant
coefficients and multiplicative time-only Gaussian white noise, and to
illustrate the results on some particular examples.
In general, there is no single condition for well-posedness
in terms of the coefficients of the equation, but
analysis of certain classes of equations leads to analogues
of the stochastic parabolicity condition.
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