Suppose that X1, . . . , Xn are continuous semimartingales that are reversible and have nondegenerate crossings. Then the corresponding rank processes can be represented by generalized Stratonovich integrals, and this representation can be used to decompose the relative log-return of portfolios generated by functions of ranked market weights. Introduction For n ≥ 2, consider a family of continu...

We present a technique, based on so-called word series, to write down in a systematic way expansions of the strong and weak local errors of splitting algorithms for the integration of Stratonovich stochastic differential equations. Those expansions immediately lead to the corresponding order conditions. Word series are similar to, but simpler than, the B-series used to analyze Runge–Kutta and o...

Abstract We review the introduction of several types projection filters. Projection structures coming from information geometry are used to obtain a finite dimensional filter in form stochastic differential equation (SDE), starting exact infinite-dimensional partial (SPDE) for optimal filter. start with Stratonovich filters based on Hellinger distance as introduced and developed Brigo et al. (I...

We derive the form of the Belavkin-Kushner-Stratonovich equation describing the filtering of a continuous observed quantum system via non-demolition measurements when the statistics of the input field used for the indirect measurement are in a general coherent state.

We define a discretized Langevin equation in Stratonovich-type calculus. We show that a generating functional with a field-dependent kernel can be written in mid-point prescription only when we calculate in the calculus. Moreover we investigate whether supersymmetry of the stochastic action with field-dependent kernel exists or not. – 1 –