arXiv subjects

Sumit Suthar

Publications and source records attributed to Sumit Suthar.

3 recordsLinked to original sources

arXiv2022

Explicitly Constrained Stochastic Differential Equations on Manifolds

In this manuscript we consider Intrinsic Stochastic Differential Equations on manifolds and constrain it to a level set of a smooth function. Such type of constraints are known as explicit algebraic constraints. The system of differential equation and the algebraic constraints is, in combination, called the Stochastic Differential Algebraic Equations (SDAEs). We consider these equations on manifolds and present methods for computing the solution of SDAEs on manifolds.

math.PR↗

arXiv2022

Intrinsic Stochastic Differential Equations and Extended Ito Formula on Manifolds

A general way of representing Stochastic Differential Equations (SDEs) on smooth manifold is based on Schwartz morphism. In this manuscript we are interested in SDEs on a smooth manifold $M$ that are driven by p-dimensional Wiener process $W_t \in \mathbb{R}^p$. In terms of Schwartz morphism, such SDEs are represented by Schwartz morphism that morphs the semi-martingale $(t,W_t)\in\mathbb{R}^{p+1}$ into a semi-martingale on the manifold $M$. We show that it is possible to construct such Schwartz morphisms using special maps that we call as diffusion generators. We show that one of the ways of constructing diffusion generator is by using regular Lagrangian. Using this diffusion generator approach, we also give extended Ito formula (also known as generalized Ito formula or Ito-Wentzell's formula) for SDEs on manifold.

math.DG↗

arXiv2021

On Explicit Stochastic Differential Algebraic Equations

Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the category of Stochastic Differential-Algebraic Equations (SDAEs). In this article, the focus is on combining ideas from the local theory of Differential-Algebraic Equations with that of Stochastic Differential Equations. The question of existence and uniqueness of the solution for SDAEs is addressed by using contraction mapping theorem in an appropriate Banach space to arrive at a sufficient condition. From the geometric point of view, a necessary condition is derived for the existence of the solution. It is observed that there exists a class of completely high index SDAEs for which there is no solution. Hence, techniques to find approximate solution of completely high index equations are presented. The techniques are illustrated with examples and numerical computations.

math.OC↗