相关论文: On the It\^o-Alekseev-Gr\"obner formula for stocha…
The Alekseev-Gr\"obner formula is a well known tool in numerical analysis for describing the effect that a perturbation of an ordinary differential equation (ODE) has on its solution. In this article we provide an extension of the…
In this paper, we establish an Alekseev--Gr\"obner formula for stochastic differential equations (SDEs) driven by a Poisson random measure, which express the global error between a functional of two processes solution of SDEs started at the…
Stochastic differential equations (SDE) are widely used in modeling stochastic dynamics in literature. However, SDE alone is not enough to determine a unique process. A specified interpretation for stochastic integration is needed.…
We provide an It\^{o}'s formula for stochastic dynamical equation on general time scales. Based on this It\^{o}'s formula we give a closed form expression for stochastic exponential on general time scales. We then demonstrate a Girsanov's…
We present a novel backward It{\^o}-Ventzell formula and an extension of the Aleeksev-Gr\"obner interpolating formula to stochastic flows. We also present some natural spectral conditions that yield direct and simple proofs of time uniform…
The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the…
A peculiar feature of It\^o's calculus is that it is an integral calculus that gives no explicit derivative with a systematic differentiation theory counterpart, as in elementary calculus. So, can we define a pathwise stochastic derivative…
An Ito formula is developed in a context consistent with the development of abstract existence and unique- ness theorems for nonlinear stochastic partial differential equations, which are singular or degenerate. This is a generalization of…
We establish It\^o's formula along flows of probability measures associated with general semimartingales; this generalizes existing results for flows of measures on It\^o processes. Our approach is to first establish It\^o's formula for…
We extend the Ito -to- Stratonovich analysis or quantum stochastic differential equations, introduced by Gardiner and Collett for emission (creation), absorption (annihilation) processes, to include scattering (conservation) processes.…
We present new stochastic differential equations, that are more general and simpler than the existing Ito-based stochastic differential equations. As an example, we apply our approach to the investment (portfolio) model.
We present a detailed analysis of non-degenerate time-homogeneous It\^o-stochastic differential equations with low local regularity assumptions on the coefficients. In particular the drift coefficient may only satisfy a local integrability…
This paper is complete proof of one method for obtaining the generalized Ito-Wentzell formula, its basic idea was announced earlier in a pre-print (arXiv:1309.3038v1). This proof sets the approach which uses the Ito formula and the…
We propose to study a new type of Backward stochastic differential equations driven by a family of It\^o's processes. We prove existence and uniqueness of the solution, and investigate stability and comparison theorem.
We introduce a Skorokhod type integral and prove an Ito formula for a wide class of Gaussian processes which may exhibit stochastic discontinuities. Our Ito formula unifies and extends the classical one for general (i.e., possibly…
The overarching goal of this paper is to establish a set-valued It\^{o}'s formula. As an application, we obtain the existence and uniqueness of solutions for the general set-valued backward stochastic differential equation which gives an…
Several versions of It\^{o}'s formula have been obtained in the context of the functional stochastic calculus. Here, we revisit this topic in two ways. First, by defining a notion of derivative along a functional, we extend the setting of…
The article is devoted to comparative analysis of the efficiency of application of Legendre polynomials and trigonometric functions to the numerical integration of Ito stochastic differential equations in the framework of the method of…
This is a survey note of the author's observations on the discrete-time analogues of It\^o formulas.
Interpreting the noise in a stochastic differential equation, in particular the It\^o versus Stratonovich dilemma, is a problem that has generated a lot of debate in the physical literature. In the last decades, a third interpretation of…