Continuous sample paths

Independence of increments

Gaussian distribution of increments

All of the above

Brownian motion

Poisson process

Geometric Brownian motion

Ornstein-Uhlenbeck process

A partial differential operator

A matrix

A function

A vector

A partial differential equation that describes the evolution of the probability density function of a diffusion process

A stochastic differential equation that describes the dynamics of a diffusion process

An integral equation that describes the transition probabilities of a diffusion process

A system of ordinary differential equations that describes the moments of a diffusion process

A formula for differentiating a function of a diffusion process

A formula for integrating a function of a diffusion process

A formula for solving a stochastic differential equation

A formula for finding the moments of a diffusion process

Modeling the stock market

Modeling the spread of a disease

Modeling the motion of a particle in a fluid

All of the above

Diffusion processes are solutions to partial differential equations

Partial differential equations are solutions to diffusion processes

Diffusion processes and partial differential equations are equivalent

Diffusion processes and partial differential equations are independent

It is the simplest diffusion process

It is the building block for more complex diffusion processes

It is the only diffusion process with independent increments

All of the above

It determines the direction of the process

It determines the rate of diffusion

It determines the variance of the process

It determines the mean of the process

Diffusion processes are a subclass of Markov processes

Markov processes are a subclass of diffusion processes

Diffusion processes and Markov processes are equivalent

Diffusion processes and Markov processes are independent

It describes the probability of transitioning from one state to another

It determines the rate of diffusion

It is related to the infinitesimal generator of the process

All of the above

Diffusion processes are solutions to stochastic differential equations

Stochastic differential equations are solutions to diffusion processes

Diffusion processes and stochastic differential equations are equivalent

Diffusion processes and stochastic differential equations are independent

It determines the rate of diffusion

It determines the direction of the process

It determines the variance of the process

It determines the mean of the process

Diffusion processes are continuous-time limits of random walks

Random walks are discrete-time limits of diffusion processes

Diffusion processes and random walks are equivalent

Diffusion processes and random walks are independent

It determines the transition probabilities of the process

It determines the rate of diffusion

It is related to the transition density function

All of the above