Introduction to Stochastic Analysis: Integrals and Differential Equations

Index

 

 

σ-algebra of subsets (events)

almost surely

approximation

Euler

Euler–Maruyama

Heun

improved Euler

Milstein

second-order

second-order for Stratonovich

equation

Milstein-type

modified trapezoidal

of adapted processes by step processes

Runge–Kutta

 

strong

weak

Borel

σ-algebra

set

boundary

attracting

natural

unattainable

Brownian motion

k-dimensional

as a Markov process

physical

Cauchy convergence criterion

central limit theorem

coefficient

diffusion

drift

comparison

of solutions

condition

linear growth

Lipschitz

of no arbitrage opportunity

conditional

density

distribution

distribution function

expectation

probability

with respect to a random variable

contingent claim

convergence

almost surely

in distribution

in probability

in the L² sense

mean square

of a series of random variables

of random processes

weak

weak of finite-dimensional

distributions

with probability one

covariation

of two Itô processes

density

of a random variable

stationary

differential

stochastic

distribution

function

of a random variable

Equation

Fokker–Planck

equation

backward Kolmogorov

Black–Scholes

Fokker–Planck

forward Kolmogorov

genetic model

Ginzburg–Landau

growth

Langevin

linear stochastic differential

stochastic differential

in the Stratonovich form

stochastic exponential

Stratonovich

reduction to Itô equation

reduction to Itô equation

Verhulst

equivalent probabilities

ergodicity

of a diffusion process

event

expectation

of a discrete random variable

of a random variable

of a solution of LSDE ...