Yuliya Mishura: Stochastic calculus for fractional processes: stochastic integration, stochastic differential equations (1/2)

Prof.ssa Yuliya Mishura

Head of the Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv

Stochastic calculus for fractional processes: stochastic integration, stochastic differential equations

Abstract: (Part I) We consider elements of fractional calculus, definition, properties and representations of fractional Brownian motion (fBm), stochastic integration with respect to fBm, stochastic differential equations with fBm. Special attention will be paid to particular equations: fractional Langevin equations, fractional Cox-Ross-Ingersoll equation. Advanced topics of fractional processes: fractional irregularity, representation results, statistical applications