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Kinetic energy of the Langevin particle
Author(s) -
Escudero Carlos
Publication year - 2020
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12333
Subject(s) - langevin equation , stochastic differential equation , statistical physics , kinetic energy , physics , particle (ecology) , interpretation (philosophy) , classical mechanics , brownian dynamics , langevin dynamics , stochastic process , brownian motion , mathematics , mathematical physics , quantum mechanics , computer science , programming language , geology , statistics , oceanography
We compute the kinetic energy of the Langevin particle using different approaches. We build stochastic differential equations that describe this physical quantity based on both the Itô and Stratonovich stochastic integrals. It is shown that the Itô equation possesses a unique solution, whereas the Stratonovich one possesses infinitely many, all but one absent of physical meaning. We discuss how this fact matches with the existent discussion on the Itô vs Stratonovich dilemma and the apparent preference toward the Stratonovich interpretation in the physical literature.