Multiple Stratonovich integrals (MSI) with respect to the Wiener process and the Brownian bridge are defined for a class of kernels having k-th order t-traces which are, in general different from the traces investigated in earlier work. Asymptotic distributions of V-statistics are derived and the limiting distribution expressed in terms of appropriate MSI. Another application yields an alternat...

We provide a detailed hands-on tutorial for the R Development Core Team [2014] add-on package Sim.DiffProc [Guidoum and Boukhetala, 2014], for symbolic and floating point computations in stochastic calculus and stochastic differential equations (SDEs). The package implement is introduced and it is explains how to use the snssde1d, snssde2d and snssde3d main functions in this package, for simula...

The diffusive dynamics of a particle in a medium with space-dependent friction coefficient is studied within the framework of the inertial Langevin equation. In this description, the ambiguous interpretation of the stochastic integral, known as the Itô-Stratonovich dilemma, is avoided since all interpretations converge to the same solution in the limit of small time steps. We use a newly develo...

We give a summary on the geometry of iterated Stratonovich integrals. For this exposition, we always have the connection to stochastic Taylor expansion in mind. In particular, we believe that “cubature on Wiener space” is best understood in the setting presented in this text. Besides cubature on Wiener space, we also give a second application regarding the heat kernel on nilpotent free Lie groups.

In this paper we extend the recent work of C.A. Braumann [1] to the case of stochastic differential equation with random coefficients. Furthermore, the relationship of the Itô-Stratonovich stochastic calculus to studies of random population growth is also explained.