The Loose Subordination of Differential Processes to Brownian Motion

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Stochastic Processes and Brownian Motion

This last point, however, raises a serious question: how well does equilibrium thermodynamics really motivate our understanding of nonequilibrium phenomena? Is it reasonable for an organometallic chemist to analyze a catalytic cycle in terms of rate-law kinetics, or for a biochemist to treat the concentration of a solute in an organelle as a bulk mixture of compounds? Under many circum­ stances...

processes and Brownian motion problems

Introduction to the theory of stochastic processes and Brownian motion problems Lecture notes for a graduate course, These notes are an introduction to the theory of stochastic processes based on several sources. The presentation mainly follows the books of van Kampen [5] and Wio [6], except for the introduction , which is taken from the book of Gardiner [2] and the parts devoted to the Langevi...

existence and measurability of the solution of the stochastic differential equations driven by fractional brownian motion

Convergence of Scaled Renewal Processes to Fractional Brownian Motion

The superposition process of independent counting renewal processes associated with a heavy-tailed interarrival time distribution is shown to converge weakly after rescaling in time and space to fractional Brownian motion, as the number of renewal processes tends to innnity. Corresponding results for continuous arrival uid processes are discussed.