scholarly journals Remarks on compositions of some random integral mappings

2018 ◽  
Vol 137 ◽  
pp. 277-282
Author(s):  
Zbigniew J. Jurek
Keyword(s):  
Random Integral

scholarly journals Surjectivity of near-square random matrices

2019 ◽  
Vol 29 (2) ◽  
pp. 267-292
Author(s):  
Hoi. H. Nguyen ◽  
Elliot Paquette
Keyword(s):  
Random Matrices ◽  
High Probability ◽  
Sparse Matrices ◽  
Integral Lattice ◽  
Integral Matrix ◽  
Random Integral ◽  
Very High ◽  
Dependent Entries ◽  
Independent And Identically Distributed

AbstractWe show that a nearly square independent and identically distributed random integral matrix is surjective over the integral lattice with very high probability. This answers a question by Koplewitz [6]. Our result extends to sparse matrices as well as to matrices of dependent entries.

Random integral guiding functions with application to random differential complementarity systems

2018 ◽  
Vol 38 (1-2) ◽  
pp. 113
Author(s):  
Tran Dinh Ke ◽  
Nguyen Van Loi ◽  
Valeri Obukhovskii ◽  
Mai Quoc Vu
Keyword(s):  
Guiding Functions ◽  
Random Integral

scholarly journals On a Coupled System of Stochastic Ito^-Differential and the Arbitrary (Fractional) Order Differential Equations with Nonlocal Random and Stochastic Integral Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2571
Author(s):  
A. M. A. El-Sayed ◽  
Hoda A. Fouad
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Integral ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Nonlocal Problems ◽  
Integral Conditions ◽  
Fractional Stochastic Differential Equations ◽  
Random Integral

The fractional stochastic differential equations had many applications in interpreting many events and phenomena of life, and the nonlocal conditions describe numerous problems in physics and finance. Here, we are concerned with the combination between the three senses of derivatives, the stochastic Ito^-differential and the fractional and integer orders derivative for the second order stochastic process in two nonlocal problems of a coupled system of two random and stochastic differential equations with two nonlocal stochastic and random integral conditions and a coupled system of two stochastic and random integral conditions. We study the existence of mean square continuous solutions of these two nonlocal problems by using the Schauder fixed point theorem. We discuss the sufficient conditions and the continuous dependence for the unique solution.

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