Show simple item record

dc.contributor.authorNualart, David
dc.contributor.authorViens, Frederi
dc.identifier.citationNualart, David; Viens, Frederi. Evolution equation of a stochastic semigroup with white-noise drift. Ann. Probab. 28 (2000), no. 1, 36--73.
dc.descriptionThis is the published version, also available here:
dc.description.abstractWe study the existence and uniqueness of the solution of a function-valued stochastic evolution equation based on a stochastic semigroup whose kernel p(s,t,y,x) is Brownian in s and t.The kernel p is supposed to be measurable with respect to the increments of an underlying Wiener process in the interval [s,t]. The evolution equation is then anticipative and, choosing the Skorohod formulation,we establish existence and uniqueness of a continuous solution with values in L2(Rd).

As an application we prove the existence of a mild solution of the stochastic parabolic equation

du_t = \Delta_x u dt + v(dt, x) \cdot \nabla u + F(t, x, u) W(dt, x),

where v and W are Brownian in time with respect to a common filtration. In this case, p is the formal backward heat kernel of Δx+v(dt,x)⋅∇x .
dc.publisherInstitute of Mathematical Statistics (IMS)en_US
dc.titleEvolution equation of a stochastic semigroup with white-noise driften_US
kusw.kuauthorNualart, David
kusw.oaversionScholarly/refereed, publisher version
kusw.oapolicyThis item does not meet KU Open Access policy criteria.

Files in this item


This item appears in the following Collection(s)

Show simple item record