6533b832fe1ef96bd129ad9f

RESEARCH PRODUCT

Set-valued stochastic integral equations driven by martingales

Marek T. MalinowskiMariusz MichtaMariusz Michta

subject

Stratonovich integralContinuous-time stochastic processApplied MathematicsMathematical analysisMathematicsofComputing_NUMERICALANALYSISStochastic calculusRiemann–Stieltjes integralRiemann integralsymbols.namesakeQuantum stochastic calculusImproper integralsymbolsDaniell integralAnalysisMathematics

description

Abstract We consider a notion of set-valued stochastic Lebesgue–Stieltjes trajectory integral and a notion of set-valued stochastic trajectory integral with respect to martingale. Then we use these integrals in a formulation of set-valued stochastic integral equations. The existence and uniqueness of the solution to such the equations is proven. As a generalization of set-valued case results we consider the fuzzy stochastic trajectory integrals and investigate the fuzzy stochastic integral equations driven by bounded variation processes and martingales.

yearjournalcountryeditionlanguage
2012-10-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2012.04.042