Modelling and Application of Stochastic Processes

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Stochastic modelling and its applications 1. This is the probabilistic counterpart to a deterministic process. Instead of describing a process which can only evolve in one way, in a stochastic or random process there is some indeterminacy: even if the initial condition is known, there are several directions in which the process may evolve. Mathematical Representation Given a probability space and a measurable space , an S-valued stochastic process is a collection of S-valued random variables on , indexed by a totally ordered set T "time".

Stochastic Modelling - Engineering Systems and Design (ESD)

That is, a stochastic process X is a collection where each is an S-valued random variable on. The space S is then called the state space of the process. Real life example of stochastic process 5. A method of financial modeling in which one or more variables within the model are random. Stochastic modeling is for the purpose of estimating the probability of outcomes within a forecast to predict what conditions might be like under different situations. The random variables are usually constrained by historical data, such as past market returns. Stochastic Modelling 6.

The probability of delivering a message with some data loss is termed as loss probability. The time between the source sending a message and the destination receiving it is called latency or delay. Re-inserting token on the ring Choices: 1. After station has completed transmission of the frame.

After leading edge of transmitted frame has returned to the sending station Depending on the network segment, all messages are broken down into either packets or cells. Packets: The length or size of a packet ranges anywhere from 60 bytes to bytes and generally follows a bimodal distribution.

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Hierarchical Networks Telecommunication networks are typically hierarchical in nature. The process of mixing is known as multiplexing. Aggregate Level Several computer, printers, etc are connected together to form a local area network LAN. For example, fluid flows at rate r 1 bytes per second for a random amount of time t1, then flows at rate r 2 bytes per second for a random amount of time t2, and so on.

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Fluid flows in the pipe at rate r Z t at time t. Fluid-flow Traffic Models ATS is subject to disturbances that change rates of aircraft flow in parts of the network. Stochastic modeling is used in a variety of industries around the world. The insurance industry, for example, relies heavily on stochastic modeling to predict how company balance sheets will look at a given point in the future.

Other sectors, industries, and disciplines that depend on stochastic modeling include stock investing, statistics, linguistics, biology, and quantum physics. Stochastic investment models attempt to forecast the variations of prices, returns on assets ROA , and asset classes—such as bonds and stocks—over time. The Monte Carlo simulation is one example of a stochastic model; it can simulate how a portfolio may perform based on the probability distributions of individual stock returns.

The significance of stochastic modeling in finance is extensive and far-reaching. When choosing investment vehicles, it is critical to be able to view a variety of outcomes under multiple factors and conditions. In some industries, a company's success or demise may even hinge on it. In the ever-changing world of investing, new variables can come into play at any time, which could affect a stockpicker's decisions enormously.

Hence, finance professionals often run stochastic models hundreds or even thousands of times, which proffers numerous potential solutions to help target decision-making.

STK2130 – Modelling by Stochastic Processes

Financial Analysis. Retirement Planning.

Week 2: Poisson Processes

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