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Ito’s formula in UMD Banach spaces and regularity of solutions of the Zakai equation
 Journal of Differential Equations, http://arxiv.org/abs/0804.0302 N.V. KRYLOV
"... Abstract. Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Itô formula is proved which is applied to prove the existence of strong solutions for a class of stochastic evolution equations in UMD Banach spaces. The abstrac ..."
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Cited by 6 (2 self)
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Abstract. Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Itô formula is proved which is applied to prove the existence of strong solutions for a class of stochastic evolution equations in UMD Banach spaces. The abstract results are applied to prove regularity in space and time of the solutions of the Zakai equation.
Almost Periodicity of Inhomogeneous Parabolic Evolution Equations
 Report No.8, Fachbereich Mathematik und Informatik, Universitat
, 2002
"... We show the (asymptotic) almost periodicity of the bounded solution to the parabolic evolution equation u (t) = A(t)u(t) +f(t) on R (on R+ ) assuming that the linear operators A(t) satisfy the `Acquistapace{Terreni' conditions, that the evolution family generated by A() has an exponential dichotom ..."
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Cited by 6 (1 self)
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We show the (asymptotic) almost periodicity of the bounded solution to the parabolic evolution equation u (t) = A(t)u(t) +f(t) on R (on R+ ) assuming that the linear operators A(t) satisfy the `Acquistapace{Terreni' conditions, that the evolution family generated by A() has an exponential dichotomy, and that R(!; A()) and f are (asymptotically) almost periodic. 1.
Rboundedness of smooth operatorvalued functions
, 2009
"... In this paper we study Rboundedness of operator families T ⊂ B(X, Y), where X and Y are Banach spaces. Under cotype and type assumptions on X and Y we give sufficient conditions for Rboundedness. In the first part we show that certain integral operator are Rbounded. This will be used to obtain R ..."
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Cited by 4 (1 self)
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In this paper we study Rboundedness of operator families T ⊂ B(X, Y), where X and Y are Banach spaces. Under cotype and type assumptions on X and Y we give sufficient conditions for Rboundedness. In the first part we show that certain integral operator are Rbounded. This will be used to obtain Rboundedness in the case that T is the range of an operatorvalued function T: Rd → B(X, Y) which is in a certain Besov space B d/r r,1 (Rd; B(X, Y)). The results will be applied to obtain Rboundedness of semigroups and evolution families, and to obtain sufficient conditions for existence of solutions for stochastic Cauchy problems.