On a martingale characterization of two-parameter Wiener process

1990 ◽  
Vol 10 (3) ◽  
pp. 263-270 ◽  
Author(s):  
Enrique M. Cabaña
Keyword(s):  
Wiener Process ◽  
Two Parameter ◽  
Martingale Characterization

Two-parameter characterization of low cycle, hysteretic fatigue data

2010 ◽  
Vol 11 (6) ◽  
pp. 449-454 ◽  
Author(s):  
Sheng Bao ◽  
Wei-liang Jin ◽  
Sidney A. Guralnick ◽  
Thomas Erber
Keyword(s):  
Fatigue Data ◽  
Two Parameter

Stochastic inclusions and set-valued stochastic equations driven by a two-parameter Wiener process

2018 ◽  
Vol 18 (06) ◽  
pp. 1850047 ◽  
Author(s):  
Mariusz Michta ◽  
Kamil Łukasz Świa̧tek
Keyword(s):  
Wiener Process ◽  
Stochastic Equation ◽  
Stochastic Equations ◽  
Continuous Selection ◽  
Attainable Sets ◽  
Multivalued Solution ◽  
Stochastic Differential Inclusions ◽  
Multivalued Solutions ◽  
Two Parameter ◽  
Selection Of

In the paper we study properties of solutions to stochastic differential inclusions and set-valued stochastic differential equations driven by a two-parameter Wiener process. We establish new connections between their solutions. We prove that attainable sets of solutions to such inclusions are subsets of values of multivalued solutions of associated set-valued stochastic equations. Next we show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set-valued stochastic equation. Additionally we establish other properties of such solutions. The results obtained in the paper extends results dealing with this topic known both in deterministic and stochastic cases.

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