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Some SDEs with distributional drift Part I: General calculus

Franco Flandoli · Francesco Russo · Jochen Wolf

45 citations0/0 files storedOsaka City University (Osaka City University)

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Mathematical and Theoretical Analysis

Abstract

Diffusions in a generalized sense were studied by several authors. First, we mention a classical book by N.I. Portenko ([21]) which, however, remains in the framework of semimartingales. The point of view adopted in this book is different from ours; its aim is to start from a Markov semigroup in order to construct solutions to some stochastic differential equations in a generalized sense. We choose to adopt a direct stochastic analysis perspective without using Markov properties. At this stage, comparing the two approaches appears to be a delicate challenge.

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References

2007Brownian Motion and Stochastic Calculus 1999Continuous Martingales and Brownian Motion 1974A TRANSFORMATION OF THE PHASE SPACE OF A DIFFUSION PROCESS THAT REMOVES THE DRIFT 1993Forward, backward and symmetric stochastic integration 1995The generalized covariation process and Ito formula 2000Stochastic calculus with respect to continuous finite quadratic variation processes 1989Strong Markov Continuous Local Martingales and Solutions of One‐Dimensional Stochastic Differential Equations (Part I)1985On solutions of one-dimensional stochastic differential equations without drift

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