TY  - JOUR
T1  - A new method for modelling the stochastic differential equations
AU  - İnce, Nihal
AU  - Şentürk, Sevil
PY  - 2025
DA  - October
Y2  - 2025
DO  - 10.15672/hujms.1637431
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 1
EP  - 19
LA  - en
AB  - This study presents a novel approach to estimate the probability density function of solutions to stochastic differential equations using generalized entropy optimization methods. Unlike traditional methods such as the Fokker–Planck–Kolmogorov equation, the proposed generalized entropy optimization methods framework accommodates cases where the distribution of the solution deviates from standard statistical forms. The method integrates the Euler–Maruyama scheme to generate multiple trajectories, producing random variables Xˆ(t) for each time t. The performance of method is evaluated through a comprehensive simulation study, in which it is compared with existing techniques under various parameter settings. Both generalized MaxEnt and MinxEnt distributions are applied, with results indicating that generalized MinxEnt distributions offer superior adaptability and accuracy. Visual and statistical comparisons confirm the theoretical validity and practical efficiency of the method. This framework not only provides a flexible alternative for probability density function estimation in stochastic differential equation modeling but also opens pathways for applications in fuzzy stochastic differential equation systems.
KW  - Euler-Maruyama method
KW  - generalized entropy optimization methods
KW  - stochastic differential equations
KW  - stochastic process
CR  - [1] C. E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27 (3), 379-423, 1948.
UR  - https://doi.org/10.15672/hujms.1637431
L1  - https://dergipark.org.tr/en/download/article-file/4598791
ER  -