Stochastic integration of functions with values in a Banach space

By J. V. Neerven, Lutz Weis. 2005

153 citations recorded by the source corpus.

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4b9e98e855e4a2e1036febeccb513e3133e13576

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. J. V. Neerven
2. Mark Veraar
3. Tuomas Hytönen
4. Lutz Weis
5. Zdzisław Brzeźniak
6. Lluís Quer-Sardanyons
7. Robert C. Dalang
8. Andrei K. Lerner

In Finance

1. J. V. Neerven
2. Mark Veraar
3. Lutz Weis
4. Tuomas Hytönen
5. Zdzisław Brzeźniak
6. Robert C. Dalang
7. Lluís Quer-Sardanyons
8. El.zbieta Motyl

In Mathematical Physics

1. J. V. Neerven
2. Tuomas Hytönen
3. Mark Veraar
4. Lutz Weis
5. Zdzisław Brzeźniak
6. Robert C. Dalang
7. Lluís Quer-Sardanyons
8. Carlos Lizama

Citations in the corpus

• Stochastic evolution equations in UMD Banach spaces (2008, result): “is finite. Here, (L2(0,t),F) denotes the Banach space of -radonifying operators fromL2(0,t) into the Banach spaceF; by the results of [ 33 ], a functionf : (0,t) ! F is stochastically integrable on (0,t) with respect to W if and only if it is the kernel of an integral operator belonging to (L2(0,t),”
• Cylindrical Lévy processes in Banach spaces (2009, unknown): “1 in [22]).”
• A T1 theorem for integral transformations with operator-valued kernel (2006, background): “This space plays a decisive rôle in the theory of stochastic integration of vector-valued functions, as recently developed in [23], [24].”
• Ito's formula in UMD Banach spaces and regularity of solutions of the Zakai equation (2008, background): “We refer to [15, 23, 24, 25] for its definition and relevant properties.”
• Continuous local martingales and stochastic integration in UMD Banach spaces (2007, background): “In [20], van Neerven and Weis have obtained necessary and sufficient conditions for stochastic integrability in terms of γ-radonifying operators in the case that M = W .”
• Maximal $L^p$-regularity for stochastic evolution equations (2011, background): “X)) of all F-adapted finite rank step processes in γ(H,X). For a detailed discussion we refer to [65]. For Banach space Xwith type 2 one has a continuous embedding L2(R +;γ(H,X)) → γ(L2(R+;H),X) (see [69, 77]). In combination with (2.4) this gives the following estimate, valid for finite rank step pro”
• Littlewood-Paley-Stein theory for semigroups in UMD spaces (2007, methodology): “It seems appropriate to comment on the relation of our Theorem 1.9 to the existence of an H∞ functional calculus for the negative generator A of P t = e−tA; this is the framework in which results similar to ours have recently been proved by Kalton and Weis [12].”
• Stochastic Integration in Banach Spaces - a Survey (2013, methodology): “The ideas of Garling and McConnell have been streamlined and extended in a systematic way by the present authors [76, 77, 83] and applied to SPDEs [12, 78, 80, 81].”
• γ-Radonifying Operators: A Survey (2010, unknown): “0 1(a,b) ⊗ (h⊗ x) dW, where the right-hand side is the side the stochastic integral for H ⊗ E-valued step functions with respect to H -cylindrical Brownian motions introduced in van Neerven and Weis [90].”
• Stochastic integrals for spde's: a comparison (2010, background): “We do not discuss Banach-space-valued stochastic integrals, for which we refer to [2] and [40].”