Is a martingale always Markov?

Martingale is a special case of Markov wth f = x and g = x. However for the process to be Markov we require for every function f a corresponding function g such that (6) holds. So not all Martingales are Markov. Similarly not all Markovs are martingales.

Does martingale have Markov property?

Any process with independent increments has the Markov property, eg Brownian motion. Martingale means that we expect the future value to be the current value. Standard Brownian motion has the Markov property and is a martingale. General Brownian motion with drift has the Markov property and is NOT a martingale.

Is A martingale stochastic?

In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values.

What is an example of a martingale that is not Markov?

This leads to the following simple example of a martingale which is not a Markov chain (of any order): Xn+1=εn+1X0+Xn. X n + 1 = ε n + 1 X 0 + X n .

Is a martingale a Markov chain?

1. Martingale is a subset of markov processes because there can be many markov processes whose expected future value is not equal to the current value.

106 (a) - Martingales

How do you determine if a chain is a Markov chain?

A Markov chain is said to be a regular Markov chain if some power of its transition matrix T has only positive entries. To determine if a Markov chain is regular, we examine its transition matrix T and powers, Tⁿ, of the transition matrix.

What are examples of not Markov chains?

Important non-Markovian processes include: ARMA (Autoregressive-moving-average) models with at least one of the two orders being greater than 1, and more complicated models in time series, such as ARCH and GARCH. All these discrete-time processes are intensively used in finance, econometrics, signal processing, etc.

Is every Brownian motion a martingale?

The Brownian motion process is a martingale: for s < t, Es(Xt ) = Es(Xs) + Es(Xt − Xs) = Xs by (iii)'.

What is not a Markov process?

Non Markovian Processes. Any process that depends on all the past states is a non Markovian process, which implies that the memory of the previously visited sites changes the distribution.

What are the flaws of martingale strategy?

Drawbacks of the Martingale Strategy

There is a chance that the stocks stop trading at some point in time. The risk-to-reward ratio of the Martingale Strategy is not reasonable. While using the strategy, higher amounts are spent with every loss until a win, and the final profit is only equal to the initial bet size.

What is the difference between Markov property and martingale?

The Markov and Martingale Properties | QuantStart. Two key concepts in quantitative finance are the Markov and Martingale properties. The former states that a given stochastic process has no "memory". The latter states that the future expectation of the process is equal to its current value.

What are the three types of martingale?

Purpose of a Martingale

There are three main types of martingales: the standing, the running, and the German martingale. Each of these three types of martingales are used in different ways, for different reasons, and in different equestrian disciplines. A martingale is used to protect both horse and rider from injury.

Is random walk a martingale?

Random Walk derives from the martingale theory. The simplest definition of random walk implies that the variation of the variable is also associated with the IID (Independently and Identically Distributed) definition of the distribution of ?_t.

Are martingales normally distributed?

Roughly speaking, (3) says that the sum of martingale differences, when scaled appropriately, is approximately normally distributed provided the conditional variances are sufficiently well behaved.

Is blackjack a Markov chain?

A game of snakes and ladders or any other game whose moves are determined entirely by dice is a Markov chain, indeed, an absorbing Markov chain. This is in contrast to card games such as blackjack, where the cards represent a 'memory' of the past moves.

How do you prove a stochastic process is a martingale?

Formally, a stochastic process as above is a martingale if E[X_t+1|ℱ_t] = X_t. Often we replace ℱ_t with the σ-algebra generated by X₀... X_t and write this as E[X_t+1|X₀... X_t] = X_t.

What are the 4 types of Markov models?

How do I know if a process is Markovian?

The most obvious way to specify a Markov process is to say what its transition probabilities are. That is, we want to know P (Xs ∈ B|Xt = x) for every s>t, x ∈ Ξ, and B ∈ X. Probability kernels (Definition 30) were invented to let us do just this.

Is Poisson a Markov process?

The Poisson process is one of the simplest examples of continuous-time Markov processes. (A Markov process with discrete state space is usually referred to as a Markov chain).

Is a Wiener process a martingale?

Proposition 178 The Wiener process is a martingale with respect to its natural filtration. Definition 179 If W(t, ω) is adapted to a filtration F and is an F-filtration, it is an F Wiener process or F Brownian motion.

Is reflected Brownian motion a martingale?

fxx(x(s))ds (16.3) 1 Page 2 2 CHAPTER 16. REFLECTED BROWNIAN MOTION is a martingale for any bounded smooth function f that is a constant (which can be taken to be 0 with out loss of generality) in some neighborhood of 0.

Why is a stochastic integral a martingale?

It is a local martingale, by definition, with quadratic variation given by Qt=∫t0H2ud<M>u. Now, QT is upper bounded by an almost surely finite random variable times <M>T. So that the expectation of the quadratic variation is finite, because M is a martingale, and hence the stochastic integral is a martingale.

What is the difference between Markov and non Markov?

Markovian will mean what may happen in the future can depend on the current position, but given that then not on the past - another word is memoryless; by contrast non-Markovian will mean that in addition to the effect of the current position, previous positions may also have an impact.

What is the difference between Markov chain and Markov process?

A Markov chain is a discrete-time process for which the future behaviour, given the past and the present, only depends on the present and not on the past. A Markov process is the continuous-time version of a Markov chain. Many queueing models are in fact Markov processes.

What is alternative to Markov model?

Time-inhomogeneous hidden Bernoulli model: An alternative to hidden Markov model for automatic speech recognition. Abstract: In this paper, a new acoustic model called time-inhomogeneous hidden Bernoulli model (TI-HBM) is introduced as an alternative to hidden Markov model (HMM) in automatic speech recognition.