# Probability theory
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1. Probability space
- Event
- Outcome
- Probability measure
- Cantelli's inequality
- Chebyshev's inequality
- Markov's inequality
- Filtration
- Filtered probability space
- Conditional probability
- Bayes' theorem
2. Random Variables
- PMF/PDF
- CDF
- MGF/CF
- Expectation
- Variance
- Kurtosis
- Skewness
- Moments
- ConditionalExpectation
- Probability distribution
- Vector RV
- JPDF/JPMF
- CPDF/CPMF
- Matrix RV
- Law of large numbers (LLN)
- Central limit theorem (CLT)
- Independence
- Correlation
- Covariance
- Covariance matrix
- Law of total probability
- Law of total expectation
- Law of total variance
- Convergence in distribution
- Convergence in probability
- Almost sure convergence
3. Stochastic processes
- Stochastic process
- Trajectory
- Increment
- Independent increments
- Gaussian process
- Gaussian process
- Wiener process
- Markov process
- Discrete time Markov process (DTMP)
- Continuous time Markov process (CTMP)
- Kolmogorov's criterion
- Transition probability
- Initial distribution
- Stationary distribution
- Homogeneous Markov process
- Birth death process
- Soujourn times
- Poisson process
- Compound Poisson process
- AR process
- MA process
- ARMA process
- Lag operator
- Lag polynomial
- Diffusion process
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- Drift coefficient
- Kolmogorov equation
- Itō integral
- Itō's lemma
- Cadlag function
- Weakly stationary
- Stationary
- Martingale process
- Upcrossings lemma
- Stationary process
- Transition density function
- Chapman-Kolmogorov equation
- Generator matrix