45R05 Random integral equations

Overview

45R05 studies random integral equations in the setting of special kinds of integral equations. Emphasis is placed on solvability, regularity, operator structure, and computationally stable representations for deterministic or stochastic models.

Related Wikipedia Page

Wikipedia search: Random integral equations

Useful Links

• Wikipedia search: Random integral equations
• Encyclopaedia of Mathematics
• arXiv: Classical Analysis and ODEs (math.CA)
• Integral Equations and Operator Theory
• Journal of Integral Equations and Applications
• Applicable Analysis

Key Ideas

• Model-specific formulation of random integral equations and associated kernels/operators
• Existence, uniqueness, and continuity under analytic or probabilistic assumptions
• Connections between theoretical criteria and practical approximation schemes

Typical Uses

Used to analyze memory effects, inverse formulations, and structured boundary phenomena where integral operators provide natural model representations.

Applications

• Physics and engineering models with hereditary or nonlocal interactions
• Stochastic and uncertainty-aware formulations in applied analysis
• Computational frameworks for inverse and parameter-identification problems

References

• Polyanin, A.D. and Manzhirov, A.V. (2008) Handbook of Integral Equations. 2nd edn. Boca Raton, FL: CRC Press.
• Tricomi, F.G. (1985) Integral Equations. New York, NY: Dover Publications.
• Kress, R. (2014) Linear Integral Equations. 3rd edn. New York, NY: Springer.

Recommended Textbooks

• Polyanin, A.D. and Manzhirov, A.V. (2008) Handbook of Integral Equations. 2nd edn. Boca Raton, FL: CRC Press.
• Tricomi, F.G. (1985) Integral Equations. New York, NY: Dover Publications.
• Kress, R. (2014) Linear Integral Equations. 3rd edn. New York, NY: Springer.