Rough Skin: An Introduction

An Introduction to Rough Paths

Abstract: This article aims to be an introduction to the theory of rough paths, in which integrals of differential forms against irregular paths and differential equations controlled by irregular paths are defined. This theory makes use of an extension of the notion of iterated integrals of the paths, whose algebraic properties appear to be fundamental. This theory is well-suited for stochastic...

Rough path analysis : An Introduction

We denote by Bp,T (Rd) the Banach space which consists of continuous paths starting at 0 with finite p-variation norm ‖ ‖p. The 1-variation norm of x is the same as the total variation of x. The p-variation norm defines a weaker topology of the C1-path space with x0 = 0. Actually it is proved that I0,T (x) is a continuous functional of x in the p-variation topology for any 1 ≤ p < 2. However it...

Rough-Neuro Computing: An Introduction

1 Machine Intelligence Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India [email protected] 2 Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Manitoba R3T 5V6, Canada [email protected] 3 Polish-Japanese Institute of Information Technology Research Center, Koszykowa 86, 02-008 Warsaw, Poland and Department of Mathematics and Com...

Rough paths: an introduction using classical analysis

In this article, we give a simple presentation of the theory of rough paths, that relies only on simple considerations on integrals along smooth paths and convergence of families of Hölder continuous functions. t. e a c L a i e r y y j n. n n i @ e f o u c n. A This version may be slightly different from the published version

Chronocoulometrical Responses at Rough Electrodes: An Introduction