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Set-valued and fuzzy stochastic integral equations driven by semimartingales under Osgood condition

Marek T. Malinowski (2015)

Open Mathematics

We analyze the set-valued stochastic integral equations driven by continuous semimartingales and prove the existence and uniqueness of solutions to such equations in the framework of the hyperspace of nonempty, bounded, convex and closed subsets of the Hilbert space L2 (consisting of square integrable random vectors). The coefficients of the equations are assumed to satisfy the Osgood type condition that is a generalization of the Lipschitz condition. Continuous dependence of solutions with respect...

Set-valued random differential equations in Banach space

Mariusz Michta (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We consider the problem of the existence of solutions of the random set-valued equation: (I) D H X t = F ( t , X t ) P . 1 , t ∈ [0,T] -a.e.; X₀ = U p.1 where F and U are given random set-valued mappings with values in the space K c ( E ) , of all nonempty, compact and convex subsets of the separable Banach space E. Under certain restrictions on F we obtain existence of solutions of the problem (I). The connections between solutions of (I) and solutions of random differential inclusions are investigated.

Singularité réelle isolée

Ahmed Jeddi (1991)

Annales de l'institut Fourier

Soit un germe de fonction analytique f : ( R n + 1 , 0 ) → ( R , 0 ) , n ≥ 1 à singularité isolée en 0 ∈ R n + 1 . Nous nous proposons d’étudier le développement asymptotique des intégrales de formes C c ∞ , de degré n , sur les fibres de f . Nous montrons que ces développements asymptotiques peuvent être décrits à partir de l’action de la monodromie sur le groupe H n de la fibre de Milnor complexe.

Solutions d'un système d'équations analytiques réelles et applications

Jean-Claude Tougeron (1976)

Annales de l'institut Fourier

On démontre que toute solution formelle y ‾ ( x ) d’un système d’équations analytiques réelles (resp. polynomiales réelles) f ( x , y ) = 0 , se relève en une solution C ∞ homotope à une solution analytique (resp. à une solution de Nash) aussi proche que l’on veut de y ‾ ( x ) pour la topologie de Krull. On utilise ce théorème pour démontrer l’algébricité (ou l’analyticité) de certains idéaux de R { x } (ou R [ [ x ] ] ), et aussi pour construire des déformations analytiques de germes d’ensembles analytiques en germes d’ensembles de Nash.

Some classes of infinitely differentiable functions

G. S. Balashova (1999)

Mathematica Bohemica

For nonquasianalytical Carleman classes conditions on the sequences { M ^ n } and { M n } are investigated which guarantee the existence of a function in C J { M ^ n } such that u(n)(a) = bn,    bnKn+1Mn,    n = 0,1,...,    aJ. Conditions of coincidence of the sequences { M ^ n } and { M n } are analysed. Some still unknown classes of such sequences are pointed out and a construction of the required function is suggested. The connection of this classical problem with the problem of the existence of a function with given trace at the boundary...

Some Fine Properties of BV Functions on Wiener Spaces

Luigi Ambrosio, Michele Miranda Jr., Diego Pallara (2015)

Analysis and Geometry in Metric Spaces

In this paper we define jump set and approximate limits for BV functions on Wiener spaces and show that the weak gradient admits a decomposition similar to the finite dimensional case. We also define the SBV class of functions of special bounded variation and give a characterisation of SBV via a chain rule and a closure theorem. We also provide a characterisation of BV functions in terms of the short-time behaviour of the Ornstein-Uhlenbeck semigroup following an approach due to Ledoux.

Some general means

Sándor, József Sándor, József, Gh. Toader (1999)

Czechoslovak Mathematical Journal

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