Results 1 to 10 of about 211,459 (306)

Mild to Classical Solutions for XVA Equations Under Stochastic Volatility [PDF]

SSRN Electronic Journal, 2021
We extend the valuation of contingent claims in presence of default, collateral and funding to a random functional setting and characterise pre-default value processes by martingales. Pre-default value semimartingales can also be described by BSDEs with random path-dependent coefficients and martingales as drivers.
Damiano Brigo, Federico Graceffa, Alexander Kalinin 0006   +2 more
core   +5 more sources

ON UNIQUENESS OF MILD SOLUTIONS FOR DISSIPATIVE STOCHASTIC EVOLUTION EQUATIONS [PDF]

Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2010
In the semigroup approach to stochastic evolution equations, the fundamental issue of uniqueness of mild solutions is often "reduced" to the much easier problem of proving uniqueness for strong solutions. This reduction is usually carried out in a formal way, without really justifying why and how one can do that.
Marinelli, Carlo, Röckner, Michael
openaire   +3 more sources

Existence of mild solutions for fractional nonautonomous evolution equations of Sobolev type with delay [PDF]

Journal of Inequalities and Applications, 2017
In this paper, we deal with a class of nonlinear fractional nonautonomous evolution equations with delay by using Hilfer fractional derivative, which generalizes the famous Riemann-Liouville fractional derivative. The definition of mild solutions for the
Haide Gou, Baolin Li
doaj   +2 more sources

Existence of Mild Solutions for Hilfer Fractional Evolution Equations with Almost Sectorial Operators

Axioms, 2022
In this paper, we obtain new sufficient conditions of the existence of mild solutions for Hilfer fractional evolution equations in the cases that the semigroup associated with an almost sectorial operator is compact as well as noncompact.
Mian Zhou, Chengfu Li, Yong Zhou
doaj   +3 more sources

Existence of Mild Solutions for Fractional Integrodifferential Equations with Hilfer Derivatives

Mathematics
In this paper, we study the existence of solutions for fractional integrodifferential equations with Hilfer derivatives. We establish some new existence theorems for mild solutions by using Schaefer’s fixed-point theorem, a measure of noncompactness, and
Mian Zhou, Yong Zhou
doaj   +2 more sources

Existence of mild solutions for fractional neutral evolution equations

Computers & Mathematics with Applications, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yong Zhou, Feng Jiao
openaire   +3 more sources

Decay mild solutions of fractional differential hemivariational inequalities

Topological Methods in Nonlinear Analysis, 2022
The goal of this paper is to consider fractional differential hemivariational inequalities (FDHVIs, for short) in the framework of Banach spaces. Our first aim is to investigate the existence of mild solutions to FDHVIs by means of a fixed point ...
Xiuwen Li, , Zhenhai Liu, , Ricai Luo,
openaire   +3 more sources

Local mild solutions and impulsive mild solutions for semilinear Cauchy problems involving lower Scorza-Dragoni multifunctions

, 2008
In this note we investigate in Banach spaces the existence of mild solutions for initial problems, also in presence of impulses, governed by semilinear differential inclusions where the non-linear part is a Scorza-Dragoni multifunction. All the results are obtained via a generalization of Artstein-Prikry selection theorem that we obtain in the first ...
CARDINALI, Tiziana, Portigiani, Francesco, RUBBIONI, Paola   +2 more
openaire   +3 more sources

Mild solutions for semilinear fractional differential equations

Electronic Journal of Differential Equations, 2009
This paper concerns the existence of mild solutions for fractional semilinear differential equation with non local conditions in the $alpha$-norm.
Gisele M. Mophou, Gaston M. N'Guerekata
doaj   +1 more source

Topological Structure of the Solution Sets for Impulsive Fractional Neutral Differential Inclusions with Delay and Generated by a Non-Compact Demi Group

Fractal and Fractional, 2022
In this paper, we give an affirmative answer to a question about the sufficient conditions which ensure that the set of mild solutions for a fractional impulsive neutral differential inclusion with state-dependent delay, generated by a non-compact semi ...
Zainab Alsheekhhussain, Ahmed Gamal Ibrahim, Akbar Ali   +2 more
doaj   +1 more source