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Stochastic Processes

Definition

(n-μ)-small

Definition

Accessible

Definition

Adapted

Definition

Aperiodic

Definition

Atom

Definition

Brownian Motion

Definition

Càdlàg

Definition

Chapman Kolmogorov Equation

Definition

Communication

Definition

Conditional Independence

Definition

Construction of Invariant measure

Definition

Continuous Martingale with Finite Variation is Constant

Definition

Continuous Time Markov Chain

Definition

Convergence to Equilibrium

Definition

Detailed Balance

Definition

Dirac Distribution

Definition

Disintegration

Definition

Dobrushin's Ergodic Coefficient

Definition

Doob's Forward Convergence Theorem

Definition

Doob's Maximal Inequalities

Definition

Doob's Optional Sampling Theorem

Definition

Doob's Upcrossing Inequality

Definition

Equivalent Bounds

Definition

Ergodic Theorem

Definition

Excursion Time

Definition

Existence of Càdlàg Version

Definition

Existence of Invariant measure

Definition

Feller condition for invariant measure

Definition

Feller Property

Definition

Filtration

Definition

Foster-Lyapunov Theorems

Definition

Gaussian Process

Definition

Harris Recurrent

Definition

Hitting Time

Definition

Holding Time

Definition

Indistinguishable

Definition

Indistinguishable

Definition

Invariant Distribution

Definition

Invariant Distribution ↔ Positive Recurrence

Definition

Invariant Distribution for CTMC

Definition

Invariant Measure

Definition

Invariant probability measure

Theorem

Ionescu Tulcea Theorem

Definition

Irreducible

Definition

Joint Markov Chain

Definition

Jump Chain

Definition

Jump Time

Definition

Kac's Lemma

Theorem

Kolmogorov Extension Theorem

Definition

Lévy's Convergence Theorems

Definition

Local Martingale

Definition

Lp Martingale

Definition

Markov chain

Definition

Markov Property

Definition

Martingale

Definition

Martingale Convergence Theorem

Definition

Martingale Equivalence for Stopping Times

Definition

MCMC

Definition

Metropolis Hastings Algorithm

Definition

Modification

Definition

Monte Carlo Method

Definition

Moving from small to petite sets

Definition

Non-Explosive

Definition

Null Recurrence

Definition

Occupation Time

Definition

Passage Time

Definition

Petite Set

Definition

Poisson Process

Definition

Positive Harris Recurrent

Definition

Positive Recurrent

Definition

Q-Matrix

Definition

Random Time

Definition

Recurrent

Theorem

Same Finite-Dimensional Distribution

Definition

Stationary

Definition

Stochastic Kernel

Definition

Stochastic Process

Definition

Stochastic Realization

Definition

Stopped Process is also R.C. Martingale

Definition

Stopping Time

Definition

Submartingale

Definition

Supermartingale

Definition

Transient

Definition

Transition Kernel

Definition

Uniquely Ergodic

Definition

Uniqueness of invariant measure

Definition

Upcrossings