TY - JOUR

T1 - On Some Properties of the Fractional Derivative of the Brownian Local Time

AU - Ибрагимов, Ильдар Абдуллович

AU - Смородина, Наталия Васильевна

AU - Фаддеев, Михаил Михайлович

PY - 2024/3/1

Y1 - 2024/3/1

N2 - Abstract: We study the properties of the fractional derivative of order of the Brownian local time with respect to the variable. This derivative is understood as the convolution of the local time with the generalized function. We show that appears naturally in Itô’s formula for the process. Using the martingale technique, we also study the limit behavior of as.

AB - Abstract: We study the properties of the fractional derivative of order of the Brownian local time with respect to the variable. This derivative is understood as the convolution of the local time with the generalized function. We show that appears naturally in Itô’s formula for the process. Using the martingale technique, we also study the limit behavior of as.

KW - fractional derivative

KW - local time

KW - stochastic processes

UR - https://www.mendeley.com/catalogue/a87e4006-d7a4-3fdd-bd97-095e2809492d/

U2 - 10.1134/s0081543824010115

DO - 10.1134/s0081543824010115

M3 - Article

VL - 324

SP - 100

EP - 114

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - 1

ER -