<p>With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations.</p><p>Rough path analysis provides the means for co...

1 Introduction.- 2 The space of rough paths.- 3 Brownian motion as a rough path.- 4 Integration against rough paths.- 5 Stochastic integration and Itôs formula.- 6 Doob-Meyer type decomposition for rough paths.- 7 Operations on controlled rough paths.- 8 Solutions to rough differential equations.- 9 Stochastic differential equations.- 10 Gaussian rough paths.- 11 Cameron-Martin regularity and appl...

1 Introduction.- 2 The space of rough paths.- 3 Brownian motion as a rough path.- 4 Integration against rough paths.- 5 Stochastic integration and Itôs formula.- 6 Doob-Meyer type decomposition for rough paths.- 7 Operations on controlled rough paths.- 8 Solutions to rough differential equations.- 9 Stochastic differential equations.- 10 Gaussian rough paths.- 11 Cameron-Martin regularity and appl...

1 Introduction.- 2 The space of rough paths.- 3 Brownian motion as a rough path.- 4 Integration against rough paths.- 5 Stochastic integration and Itôs formula.- 6 Doob-Meyer type decomposition for rough paths.- 7 Operations on controlled rough paths.- 8 Solutions to rough differential equations.- 9 Stochastic differential equations.- 10 Gaussian rough paths.- 11 Cameron-Martin regularity and appl...

1 Introduction.- 2 The space of rough paths.- 3 Brownian motion as a rough path.- 4 Integration against rough paths.- 5 Stochastic integration and Itôs formula.- 6 Doob-Meyer type decomposition for rough paths.- 7 Operations on controlled rough paths.- 8 Solutions to rough differential equations.- 9 Stochastic differential equations.- 10 Gaussian rough paths.- 11 Cameron-Martin regularity and appl...

With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations.Rough path analysis provides the means for constructing...

With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations.Rough path analysis provides the means for constructing...

1 Introduction.- 2 The space of rough paths.- 3 Brownian motion as a rough path.- 4 Integration against rough paths.- 5 Stochastic integration and Itôs formula.- 6 Doob-Meyer type decomposition for rough paths.- 7 Operations on controlled rough paths.- 8 Solutions to rough differential equations.- 9 Stochastic differential equations.- 10 Gaussian rough paths.- 11 Cameron-Martin regularity and appl...