The Möbius-transformed trapezoidal rule achieves optimal convergence rates for polynomially weighted integrals on the real line when the integrand belongs to a corresponding weighted Sobolev space of positive integer smoothness, with a weaker extension to fractional smoothness.
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Occupied processes augment Markov processes with occupation flows to enable Markovian lifts and an Ito calculus for path-dependent PDEs where occupation acts as time.
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M\"obius-transformed trapezoidal rule for polynomial weights
The Möbius-transformed trapezoidal rule achieves optimal convergence rates for polynomially weighted integrals on the real line when the integrand belongs to a corresponding weighted Sobolev space of positive integer smoothness, with a weaker extension to fractional smoothness.
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Occupied Processes: Going with the Flow
Occupied processes augment Markov processes with occupation flows to enable Markovian lifts and an Ito calculus for path-dependent PDEs where occupation acts as time.