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Watershed Planning within a Quantitative Scenario Analysis Framework
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A discrete algebraic framework for stochastic systems which yield unique and exact solutions.

Michelle Rudolph-Lilith1

  • 1Unité de Neurosciences, Information et Complexité (UNIC), CNRS, Gif-sur-Yvette, France.

Heliyon
|August 11, 2018
PubMed
Summary

This study identifies ambiguity in stochastic calculus and proposes a discrete algebraic framework. This new framework offers unique, exact solutions for stochastic models, potentially solving a broader range of problems.

Keywords:
Applied mathematicsStatistical physics

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Area of Science:

  • Physical Systems Dynamics
  • Stochastic Modeling
  • Mathematical Physics

Background:

  • Physical systems often display inherent randomness, influencing their behavior.
  • Stochastic calculus provides a mathematical framework for analyzing these systems, but can yield ambiguous results.
  • Current numerical methods and existing calculus frameworks have limitations in providing definitive solutions.

Purpose of the Study:

  • To identify the conceptual issues causing ambiguity in traditional stochastic calculus.
  • To introduce a novel discrete algebraic framework for analyzing stochastic models.
  • To demonstrate the framework's capability for generating unique and exact solutions.

Main Methods:

  • Conceptual analysis of the foundations of stochastic calculus.
  • Development of a discrete algebraic framework.
  • Application of the framework to representative stochastic models.

Main Results:

  • Pinpointed the source of ambiguity within the analytical underpinnings of stochastic calculus.
  • Demonstrated a discrete algebraic approach yielding unambiguous solutions.
  • Showcased the framework's potential for broader applicability to diverse stochastic models.

Conclusions:

  • The proposed discrete algebraic framework resolves ambiguities inherent in stochastic calculus.
  • This novel approach provides exact and unique solutions for stochastic dynamic systems.
  • The framework holds promise for advancing the analysis of a wider array of stochastic models.