Understanding stochastic differential equations
Pat Muldowney
TL;DR
This paper provides an in-depth discussion of stochastic differential equations and integrals, framing them within Riemann-Stieltjes integration to clarify their mathematical foundations.
Contribution
It offers a conceptual clarification and contextualization of stochastic differential equations and integrals, supplementing existing literature.
Findings
Clarifies the meaning of stochastic differential equations
Connects stochastic integrals with Riemann-Stieltjes integration
Provides insights as a supplement to prior work
Abstract
This essay explores the meaning of stochastic differential equations and stochastic integrals. It sets these subjects in a context of Riemann-Stieltjes integration. It is intended as a comment or supplement to \cite{MTRV}.
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Taxonomy
TopicsStochastic processes and financial applications · Nonlinear Differential Equations Analysis · Quantum chaos and dynamical systems