Generalized random processes and Cauchy′s problem for some partial differential systems
International Journal of Mathematics and Mathematical Sciences, Volume 3, Issue 3, Page 549-558, 1980., 1979 In this paper we consider a parabolic partial differential system of the form DtHt = L(t, x, D)Ht. The generalized stochastic solutions Ht, corresponding to the generalized stochastic initial conditions H0 are given. Some properties concerning these generalized stochastic solutions are also obtained.
Mahmoud M. El-Borai
wiley +1 more source
Small noise asymptotic expansions for stochastic pde's.i : The case of a dissipative polynomially bounded non linearity [PDF]
, 2010 We study a reaction-diusion evolution equation perturbed by a Gaussian noise. Here the leading operator is the innitesimal generator of a C0-semigroup of strictly negative type, the nonlinear term has at most polynomial growth and is such that the whole ...
Albeverio, Sergio +4 more
core +1 more source
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
doaj +1 more source
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
core +1 more source
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
doaj +1 more source
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.
core
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
doaj +1 more source
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
core
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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