document

Non-autonomous stochastic Cauchy problems in Banach spaces

Veraar, M.C. (author), Zimmerschied, J. (author)

journal article 2008

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A preferential attachment model with random initial degrees

Deijfen, M. (author), Van den Esker, H. (author), Van der Hofstad, R. (author), Hooghiemstra, G. (author)

In this paper, a random graph process {G(t)} (ta parts per thousand yen1) is studied and its degree sequence is analyzed. Let {W (t) } (ta parts per thousand yen1) be an i.i.d. sequence. The graph process is defined so that, at each integer time t, a new vertex with W (t) edges attached to it, is added to the graph. The new edges added at time t...

journal article 2008

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A note on optimal probability lower bounds for centered random variables

Veraar, M.C. (author)

journal article 2008

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A Clark-Occone formula in UMD Banach spaces

Maas, J. (author), Van Neerven, J.M.A.M. (author)

journal article 2008

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The Vector-Valued Big q -Jacobi Transform

Groenevelt, W. (author)

Big q-Jacobi functions are eigenfunctions of a second-order q-difference operator L. We study L as an unbounded self-adjoint operator on an L-2-space of functions on R with a discrete measure. We describe explicitly the spectral decomposition of L using an integral transform F with two different big q-Jacobi functions as a kernel, and we...

journal article 2008

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Ito's formula in UMD Banach spaces and regularity of solution of the Zakai equation

Brzezniak, Z. (author), Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author)

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...

journal article 2008

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The backward Îto method for the Lagrangian simulation of transport processes with large space variations of the diffusivity

Spivakovskaya, D. (author), Heemink, A.W. (author), Deleersnijder, E. (author)

Random walk models are a powerful tool for the investigation of transport processes in turbulent flows. However, standard random walk methods are applicable only when the flow velocities and diffusivity are sufficiently smooth functions. In practice there are some regions where the rapid but continuous change in diffusivity may be represented by...

journal article 2007

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Continuous local martingales and stochastic integration in UMD Banach spaces

Veraar, M.C. (author)

Recently, van Neerven, Weis and the author, constructed a theory for stochastic integration of UMD Banach space valued processes. Here the authors use a (cylindrical) Brownian motion as an integrator. In this note we show how one can extend these results to the case where the integrator is an arbitrary real-valued continuous local martingale. We...

journal article 2007

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On Positivity for the Biharmonic Operator under Steklov Boundary Conditions

Gazzola, F. (author), Sweers, G. (author)

The positivity-preserving property for the inverse of the biharmonic operator under Steklov boundary conditions is studied. It is shown that this property is quite sensitive to the parameter involved in the boundary condition. Moreover, positivity of the Steklov boundary value problem is linked with positivity under boundary conditions of Navier...

journal article 2007

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Conditions for stochastic integrability in UMD Banach spaces

Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author)

conference paper 2007

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On analytic Ornstein-Uhlenbeck semigroups in infinite dimensions

Maas, J. (author), Van Neerven, J.M.A.M. (author)

We extend to infinite dimensions an explicit formula of Chill, Fasangová, Metafune, and Pallara for the optimal angle of analyticity of analytic Ornstein-Uhlenbeck semigroups. The main ingredient is an abstract representation of the Ornstein-Uhlenbeck operator in divergence form.

journal article 2007

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Continuous/discrete non parametric Bayesian belief nets with UNICORN and UNINET

Cooke, R.M. (author), Kurowicka, D. (author), Hanea, A.M. (author), Morales Napoles, O. (author), Ababei, D.A. (author), Ale, B.J.M. (author), Roelen, A. (author)

Hanea et al. (2006) presented a method for quantifying and computing continuous/discrete non parametric Bayesian Belief Nets (BBN). Influences are represented as conditional rank correlations, and the joint normal copula enables rapid sampling and conditionalization. Further mathematical background is in Kurowicka and Cooke (2007). This article...

conference paper 2007

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Distribution of Global Measures of Deviation Between the Empirical Distribution Function and Its Concave Majorant

Kulikov, V.N. (author), Lopuhaä, H.P. (author)

We investigate the distribution of some global measures of deviation between the empirical distribution function and its least concave majorant. In the case that the underlying distribution has a strictly decreasing density, we prove asymptotic normality for several L k -type distances. In the case of a uniform distribution, we also establish...

journal article 2007

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Accurate Evaluation of European and American Options Under the CGMY Process

Almendral, A. (author), Oosterlee, C.W. (author)

A finite?difference method for integro?differential equations arising from Lévy driven asset processes in finance is discussed. The equations are discretized in space by the collocation method and in time by an explicit backward differentiation formula. The discretization is shown to be second?order accurate for a relevant parameter range...

journal article 2007

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Stochastic integration in UMD Banach spaces

Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author)

journal article 2007

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Some remarks on tangent martingale difference sequences in L1-spaces

Cox, S. (author), Veraar, M. (author)

journal article 2007

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A Phase Transition for the Diameter of the Configuration Model

Van der Hofstad, R. (author), Hooghiemstra, G. (author), Znamenski, D. (author)

In this paper, we study the configuration model (CM) with independent and identically-distributed (i.i.d.) degrees. We establish a phase transition for the diameter when the power-law exponent ? of the degrees satisfies ? ? (2, 3). Indeed, we show that for ? > 2 and when vertices with degree 1 or 2 are present with positive probability, the...

journal article 2007

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Lateral entrapment of sediment in tidal estuaries: An idealized model study

Huijts, K.M.H. (author), Schuttelaars, H.M. (author), De Swart, H.E. (author), Valle-Levinson, A. (author)

Two physical mechanisms leading to lateral accumulation of sediment in tidally dominated estuaries are investigated, involving Coriolis forcing and lateral density gradients. An idealized model is used that consists of the three?dimensional shallow water equations and sediment mass balance. Conditions are assumed to be uniform in the along...

journal article 2006

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Space-time regularity of solutions of the parabolic stochastic Cauchy problem

Dettweiler, J. (author), Van Neerven, J.M.A.M. (author), Weis, L. (author)

journal article 2006

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Randomized UMD Banach spaces and decoupling

Veraar, M.C. (author)

In this paper we prove the equivalence of decoupling inequalities for stochastic integrals and one-sided randomized versions of the UMD property of a Banach space as introduced by Garling.

journal article 2006