Pathwise local well-posedness of stochastic nonlinear wave equations with multiplicative noise is established in optimal regularity ranges by unifying Fourier restriction norm methods with rough path integration.
arXiv preprint arXiv:1406.7748 , year=
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abstract
Rough sheets are two-parameter analogs of rough paths. In this work the theory of integration over functions of two parameters is extended to cover the case of irregular functions by developing an appropriate notion of rough sheet. The main application is to give a path by path construction of the stochastic integral in the plane and obtain a stratonovich change of variables formula.
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Signature kernel and Schwinger-Dyson kernel equations are recast as two-parameter rough differential equations with well-posedness, stability, and a numerical scheme established for rough driving signals.
A new strategy using controlled-path Taylor expansions yields the planar change-of-variable formula for paths with γ1 > 1/3 and γ2 > 1/2 as an explicit Riemann-sum limit, minimizing required iterated integrals.
citing papers explorer
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Fourier restriction norm method adapted to controlled paths: stochastic wave equations
Pathwise local well-posedness of stochastic nonlinear wave equations with multiplicative noise is established in optimal regularity ranges by unifying Fourier restriction norm methods with rough path integration.
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Signature Kernel and Schwinger-Dyson Kernel Equations as Two-Parameter Rough Differential Equations
Signature kernel and Schwinger-Dyson kernel equations are recast as two-parameter rough differential equations with well-posedness, stability, and a numerical scheme established for rough driving signals.
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On It\^o-Stratonovich formula for rough sheets
A new strategy using controlled-path Taylor expansions yields the planar change-of-variable formula for paths with γ1 > 1/3 and γ2 > 1/2 as an explicit Riemann-sum limit, minimizing required iterated integrals.