Steven D. Miller

collaborators

3 papers

math.PR2025

The Kelly Criterion And Utility Function Optimisation For Stochastic Binary Games: Submartingale And Supermartingale Regimes

Steven D Miller

A reformulation of the Kelly Criterion is presented. Let $G$ be a generic stochastic Bernoulli binary game with outcomes $Z (I) \in {- 1, 1}$ of N tria…

physics.flu-dyn2023

Second And Third-Order Structure Functions Of An 'Engineered' Random Field And Emergence Of The Kolmogorov 4/5 And 2/3-Scaling Laws Of Turbulence

Steven D Miller

The 4/5 and 2/3 laws of turbulence can emerge from a theory of 'engineered' random vector fields $X_{i} (x, t) = X_{i} (x, t) + \frac{θ}{d ( d + 2 )} X_{i} (x, t) ψ (x)$ existing w…

math.PR2023

A Cluster Expansion Proof That The Stochastic Exponential Of A Brownian Motion Is A Martingale

Steven D Miller

Let $ψ : R^{+} \to R^{+}$ be a smooth and continuous real function and $ψ \in L^{2} (R^{+})$ . Let $B (t)$ be a standard Brownian motion define…