Integration with respect to local time

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Strong Solutions of Mean-Field Stochastic Differential Equations with irregular drift (2018, methodology): “Similar to [2] we provide a probabilistic representation of the Malliavin derivative using the local time-space integral introduced in [17].”
Elements of Stochastic Calculus via Regularization (2006, methodology): “This approach constitutes a counterpart of a discretization approach initiated by Föllmer ( [19]) and continued by many authors, see for instance [2, 21, 14, 13, 10, 22].”
Local time–space stochastic calculus for Lévy processes (2006, methodology): “of linear Brownian motion, we show in this paper that the above formulas can be derived from the following Itô formula established in [5] F(X t , t) = F(X0, 0) + ∫ t 0 ∂ F ∂t (Xs, s) ds + ∫ t 0 ∂ F ∂x (Xs, s) dXs”
A Change-of-Variable Formula with Local Time on Curves (2005, background): “Finally, if either of the following two sets of conditions is satisfied: (3.31) s 7!”
Sobolev differentiable stochastic flows for SDEs with singular coefficients: Applications to the transport equation (2012, background): “ded measurable function f : [0,1] × R−→ Rwith respect to the local time LXx(ds,dy) of Xx := X0,x (in time and space). For more information about local time-space integration the reader is referred to [6] or [33]. We also need the following auxiliary result: Lemma 27 Let b : R−→ R be a bounded Borel ”