Cable equation with a general stochastic measure

DOI10.1090/S0094-9000-2012-00856-9zbMath1274.60159OpenAlexW2053027176MaRDI QIDQ2849254

Vadym M. Radchenko

Publication date: 17 September 2013

Published in: Theory of Probability and Mathematical Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0094-9000-2012-00856-9

zbMATH Keywords

mild solutionstochastic partial differential equationstochastic measurestochastic cable equation

Mathematics Subject Classification ID

Stochastic integrals (60H05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Random measures (60G57)

Related Items (4)

Comparison theorem for solutions of parabolic stochastic equations with an absorber ⋮ Heat equation in a multidimensional domain with a general stochastic measure ⋮ Approximation of solution of the cable equation driven by a stochastic measure ⋮ Averaging principle for a stochastic cable equation

Cites Work

• The interspike interval of a cable model neuron with white noise input
• Approximation and support theorem in Hölder norm for parabolic stochastic partial differential equations
• Dynkin's isomorphism theorem and the stochastic heat equation
• Properties of integrals with respect to a general stochastic measure in a stochastic heat equation
• Mild solution of the heat equation with a general stochastic measure
• Heat equation and wave equation with general stochastic measures
• Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion
• Quantum cable equations in terms of generalized operators
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