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Hi,

Regarding Martingales you an can see them as fair games This means that if the (martingale) process represents your gain(random) wealth, you should not be able to design a strategy to increase your current gain wealth, no matter what the outcome of the sample space is. And this property is stable.

Brownian Motion can be seen as a limit of rather simple random walks but I m I'm sure that you know about this.

Markov processes "disconnect" Future and Past of the process conditionnally on the present value of the process. Where disconnect "disconnect" means that functions of past and of future values of the process are independent condionnally conditionnally on the present value of the process.

Does it make things more clear ?
show/hide this revision's text 2 edited body

Hi,

Regarding Martingales you an see them as fair games This means that if the (martingale) process represents your gain, you should not be able to design a strategy to increase your current gain no matter what the outcome of the sample space is. And this property is stable.

Bronwian

Brownian Motion can be seen as a limit of rather simple random walks but I m sure that you know about this.

Markov processes "disconnect" Future and Past conditionnally on the present. Where disconnect means that functions of past and of future values of the process are independent condionnally on the present value of the process.

Does it make things more clear ?
show/hide this revision's text 1 [made Community Wiki]

Hi,

Regarding Martingales you an see them as fair games This means that if the (martingale) process represents your gain, you should not be able to design a strategy to increase your current gain no matter what the outcome of the sample space is. And this property is stable.

Bronwian Motion can be seen as a limit of rather simple random walks but I m sure that you know about this.

Markov processes "disconnect" Future and Past conditionnally on the present. Where disconnect means that functions of past and of future values of the process are independent condionnally on the present value of the process.

Does it make things more clear ?