Download An Introduction to Continuous-Time Stochastic Processes: by Vincenzo Capasso, David Bakstein PDF

By Vincenzo Capasso, David Bakstein

This concisely written ebook is a rigorous and self-contained advent to the speculation of continuous-time stochastic tactics. A stability of concept and purposes, the paintings positive factors concrete examples of modeling real-world difficulties from biology, drugs, commercial functions, finance, and assurance utilizing stochastic equipment. No past wisdom of stochastic strategies is required.

Key issues coated include:

* Interacting debris and agent-based types: from polymers to ants

* inhabitants dynamics: from beginning and demise tactics to epidemics

* monetary industry types: the non-arbitrage precept

* Contingent declare valuation types: the risk-neutral valuation thought

* probability research in assurance

An creation to Continuous-Time Stochastic Processes can be of curiosity to a huge viewers of scholars, natural and utilized mathematicians, and researchers or practitioners in mathematical finance, biomathematics, biotechnology, and engineering. appropriate as a textbook for graduate or complicated undergraduate classes, the paintings can also be used for self-study or as a reference. necessities contain wisdom of calculus and a few research; publicity to likelihood will be beneficial yet now not required because the useful basics of degree and integration are provided.

Show description

Read or Download An Introduction to Continuous-Time Stochastic Processes: Theory, Models, and Applications to Finance, Biology, and Medicine PDF

Similar game theory books

Algorithmic Game Theory

Within the previous couple of years online game idea has had a considerable impression on desktop technological know-how, in particular on net- and e-commerce-related concerns. greater than forty of the head researchers during this box have written chapters that cross from the principles to the cutting-edge. uncomplicated chapters on algorithmic tools for equilibria, mechanism layout and combinatorial auctions are by means of chapters on incentives and pricing, rate sharing, details markets and cryptography and protection.

The Theory of Search Games and Rendezvous (International Series in Operations Research & Management Science)

The speculation of seek video games and Rendezvous widens the size to the classical challenge with the addition of an autonomous participant of equivalent prestige to the searcher, who cares approximately being came across or no longer being came across. those a number of explanations of searcher and hider are analytically and mathematically thought of within the book's foci: seek video games (Book I) and Rendezvous concept (Book II).

The Market Approach to Comparable Company Valuation (ZEW Economic Studies)

Company valuation utilizing multiples is likely one of the most well liked company valuation ways. during this ebook, the various steps of this valuation procedure reminiscent of the choice of similar businesses or the alternative of the reference variables are mentioned. Then, the conditions required for a legitimate valuation (e.

Ad Hoc Networks Telecommunications and Game Theory

Random SALOHA and CSMA protocols which are used to entry MAC in advert hoc networks are very small in comparison to the a number of and spontaneous use of the transmission channel. in order that they have low immunity to the issues of packet collisions. certainly, the transmission time is the serious think about the operation of such networks.

Extra resources for An Introduction to Continuous-Time Stochastic Processes: Theory, Models, and Applications to Finance, Biology, and Medicine

Sample text

Two real-valued stochastic processes (Xt )t∈R+ and (Yt )t∈R+ on the probability space (Ω, F, P ) are called modifications or versions of one another if, for any t ∈ T, P (Xt = Yt ) = 1. 15. It is obvious that two processes that are modifications of one another are also equivalent. An even more stringent requirement comes from the following definition. 16. Two processes are indistinguishable if P (Xt = Yt , ∀t ∈ R+ ) = 1. 17. It is obvious that two indistinguishable processes are modifications of each other.

Furthermore, if H : (E, B) → (R, BR ), then Y ∈ L1 (P ) is equivalent to H ∈ L1 (PX ) and E[Y ] = H(x)PX (dx). 83. Let X = (X1 , X2 ) be a random vector defined on (Ω, F, P ) whose components are valued in (E1 , B1 ) and (E2 , B2 ), respectively. If h : (E1 × E2 , B1 ⊗ B2 ) → (R, BR ), then Y = h(X) ≡ h ◦ X is a real-valued random variable. Moreover, E[Y ] = h(x1 , x2 )dPX (x1 , x2 ), where PX is the joint probability of X1 and X2 . 84. If X1 and X2 are real-valued independent random variables on (Ω, F, P ) and endowed with finite expectations, then their product X1 X2 ∈ L1 (Ω, F, P ) and E[X1 X2 ] = E[X1 ]E[X2 ].

8), for all random variables X ∈ L2 (Ω, F , P ), it holds that E[XY ] = E[XE[Y |F ]], completing the proof, by remembering that (X, Y ) → E[XY ] is the scalar product in L2 . 132. We may interpret the theorem above by stating that E[Y |F ] is the best mean square approximation in L2 (Ω, F , P ) of Y ∈ L2 (Ω, F, P ). 6 Conditional and Joint Distributions Let (Ω, F, P ) be a probability space, X : (Ω, F, P ) → (E, B) a random variable, and F ∈ F. Following previous results, a unique element E[IF |X = x] ∈ L1 (E, B, PX ) exists such that for any B ∈ B P (F ∩ [X ∈ B]) = [X∈B] E[IF |X = x]dPX (x).

Download PDF sample

Rated 4.32 of 5 – based on 41 votes