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Local martingaleMartingale pricingMartingaleDoob's martingale inequalityQuadratic variationRegular conditional probabilityMarkov modelMultinomial distributionMethod of momentsMarkov decision processEmpirical measureDiffusion processStochastic matrixProbability theoryStochastic discount factorLarge deviations theoryCovarianceBranching processSemimartingaleStochastic processGirsanov theoremConditional dependenceAzuma's inequalityLaw of total probabilityBranching random walkMarkov chain monte carloChi distributionMutual informationProbability mass functionNormalizing constantDerivationConvergence of measuresConditional varianceLaw of the iterated logarithmLogistic distributionRate functionDistribution functionLogit-normal distributionRandom measureGamma distributionPairwise independenceFeller processProbability distributionProbitRayleigh distributionMean value theoremControl variatesProbability-generating functionStochastic calculusDifferential operatorMultivariate t-distributionStationary phase approximationDiscrete-time fourier transformPointwise convergenceMartingale representation theoremBalance equationStochastic driftMonotone class theoremReciprocal distributionMarginal distributionTail dependenceArithmetic progressionFunctional calculusMills ratioEmpirical processAsymptotic distributionFolded normal distributionProbability measureDiscrete poisson equationLog probabilityPointwise mutual informationStationary ergodic processDirichlet-multinomial distributionF-divergenceGeneralized pareto distributionStatistical learning theoryLinear probability modelExponential familyMixtureRecurrence relationMarkov propertyHofstadter sequenceOptional stopping theoremStochastic volatilityConvergence of random variablesCharacteristic functionNatural exponential familyAsymptotic analysisCorrelation functionAlgorithmic probabilityExponential mapBayesian gameDifferential equationMarkov chainScale parameterNakagami distributionSymmetric derivativeDivisor functionMultivariate laplace distributionLog-cauchy distribution