Brownian tsab ntawv tsa suab nyob hauv kev sib tshuam ntawm ob peb yam tseem ceeb ntawm cov txheej txheem. Nws yog a Gaussian Markov txheej txheem, nws muaj txoj hauv kev txuas mus ntxiv, nws yog txheej txheem nrog kev ywj pheej nce ntxiv (tus txheej txheem Lévy), thiab nws yog martingale. Ntau tus yam ntxwv raug paub raws li cov khoom no.
Puas yog Brownian motion txuas ntxiv lossis tsis sib cais?
Ib tus qauv d-dimensional Brownian motion yog Rd-valued continuous-time txheej txheem stochastic {Wt}t≥0 (ie, ib tsev neeg ntawm d-dimensional random vectors Wt indexed los ntawm cov txheej ntawm cov zauv tiag tiag t) nrog cov khoom nram qab no.
Puas yog Brownian motion txuas ntxiv?
Raws li peb tau pom, txawm tias Brownian motion yog nyob txhua qhov chaw txuas ntxiv, nws tsis txawv qhov twg. Qhov randomness ntawm Brownian tsab ntawv tsa suab txhais tau hais tias nws tsis coj zoo txaus los ua ke los ntawm cov txheej txheem ib txwm muaj.
Puas yog Brownian motion stochastic?
Brownian tsab ntawv tsa suab yog los ntawm far the most important stochastic process. Nws yog cov txheej txheem ntawm Gaussian, ntawm lub sijhawm txuas ntxiv martingales, thiab ntawm Markov cov txheej txheem.
Markovian kev xav yog dab tsi?
1. Qhov xwm txheej tshwm sim ntawm lub xeev tam sim no yog ywj siab ntawm txhua tus tsis yog niam txiv. Nws txhais tau tias rau lub cev muaj zog uas tau muab rau lub xeev tam sim no, txhua lub xeev hauv qab no yog ywj siab ntawm txhua lub xeev yav dhau los.
