Optimizing the Fractional Power in a Model with Stochastic PDE Constraints
Advanced Nonlinear Studies, 2018 We study an optimization problem with SPDE constraints, which has the peculiarity that the control parameter s is the s-th power of the diffusion operator in the state equation.
Geldhauser Carina, Valdinoci Enrico
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Mixing via controllability for randomly forced nonlinear dissipative PDEs [PDF]
, 2019 We continue our study of the problem of mixing for a class of PDEs with very degenerate noise. As we established earlier, the uniqueness of stationary measure and its exponential stability in the dual-Lipschitz metric holds under the hypothesis that the ...
Vahagn Nersesyan +5 more
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Solution theory of fractional SDEs in complete subcritical regimes
Forum of Mathematics, SigmaWe consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense.
Lucio Galeati, Máté Gerencsér
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The obstacle problem for semilinear parabolic partial integro-differential equations
, 2015 International audienceWe give a probabilistic interpretation for the weak Sobolev solution of obstacle problem for semilinear parabolic partial integro-differential equations (PIDE).
Matoussi, Anis +2 more
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Sub- and Super-solutions of a Nonlinear PDE, and Application to a Semilinear SPDE [PDF]
, 2013 2010 Mathematics Subject Classification: 35R60, 60H15, 74H35.We obtain upper and lower bounds for the explosion time of a semi-linear heat equation on a bounded $d$-dimensional domain, perturbed by white noise. The bounds we get are expressed in terms of
Kolkovska, E. T., López-Mimbela, J. A.
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Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations [PDF]
, 2011 MSC 2010: 26A33, 35R11, 35R60, 35Q84, 60H10 Dedicated to 80-th anniversary of Professor Rudolf GorenfloThere is a well-known relationship between the Itô stochastic differential equations (SDEs) and the associated partial differential equations called ...
Hahn, Marjorie, Umarov, Sabir
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Early warning signs for SPDEs with continuous spectrum
European Journal of Applied MathematicsIn this work, we study early warning signs for stochastic partial differential equations (SPDEs), where the linearisation around a steady state is characterised by continuous spectrum. The studied warning sign takes the form of qualitative changes in the
Paolo Bernuzzi +2 more
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Linear-implicit strong schemes for Itô-Galkerin approximations of stochastic PDEs
, 2010 Linear-implicit versions of strong Taylor numerical schemes for finite dimensional Itô stochastic differential equations (SDEs) are shown to have the same order as the original scheme.
Shott, Stephen, Kloeden, Peter E.
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A branching particle approximation to a filtering micromovement model of asset price
Particle filters, Monte Carlo approximation, Filtering, Counting process, Stochastic partial differential equation, Ultra-high frequency data, Primary: 60H15, Secondary: 60K35, 35R60, 93E11, 60F05, 91B28,
Jie Xiong, Yong Zeng
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Finite Width For A Random Stationary Interface [PDF]
, 1997 : We study the asymptotic shape of the solution u(t; x) 2 [0; 1] to a one-dimensional heat equation with a multiplicative white noise term. At time zero the solution is an interface, that is u(0; x) is 0 for all large positive x and u(0; x) is 1 for all
R. Tribe, C. Mueller
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