A Causal Construction of Diffusion Processes
Tadeusz Banek
TL;DR
This paper introduces a causal, iterative construction method for diffusion processes using a nonlinear integral equation, avoiding stochastic integrals, with applications in finance and extensions to fractional Brownian motion.
Contribution
It presents a novel causal construction of diffusion processes via a nonlinear integral equation, simplifying implementation and enabling new applications.
Findings
Provides a new iterative method for diffusion processes
Applicable to financial modeling scenarios
Extensible to fractional Brownian motion
Abstract
A simple nonlinear integral equation for Ito's map is obtained. Although, it does not include stochastic integrals, it does give causal construction of diffusion processes which can be easily implemented by iteration systems. Applications in financial modelling and extension to fBm are discussed.
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Taxonomy
TopicsStochastic processes and financial applications