By Vincenzo Capasso, David Bakstein

ISBN-10: 0817632344

ISBN-13: 9780817632342

ISBN-10: 0817644288

ISBN-13: 9780817644284

This concisely written booklet is a rigorous and self-contained advent to the speculation of continuous-time stochastic methods. A stability of conception and functions, the paintings positive aspects concrete examples of modeling real-world difficulties from biology, drugs, commercial functions, finance, and coverage utilizing stochastic equipment. No past wisdom of stochastic techniques is required.

Key issues lined include:

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

* inhabitants dynamics: from beginning and demise methods to epidemics

* monetary industry versions: the non-arbitrage precept

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

* probability research in coverage

An creation to Continuous-Time Stochastic Processes could be of curiosity to a large 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 no longer required because the worthy basics of degree and integration are provided.

Show description

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

Similar game theory books

Chance: The Life of Games and the Game of Life

With its many easy-to-follow mathematical examples, this publication takes the reader on a virtually chronological journey throughout the interesting and outstanding legislation of probability, omnipresent within the wildlife and in our day-by-day lives. alongside the course many desirable issues are mentioned, equivalent to: hard chance paradoxes; "paranormal" coincidences; video game odds; motives and results; interpretation of opinion polls; profitable percentages as a video game proceeds; the character of randomness; entropy and randomness; randomness in lifestyles; algorithmic complexity and the undecidability of randomness; chances and obstacles of studying the legislation of a Universe immersed in likelihood occasions.

Discrete Dynamical Systems

This publication presents an creation to discrete dynamical structures -- a framework of research regularly occurring within the fields of biology, demography, ecology, economics, engineering, finance, and physics. The ebook characterizes the basic elements that govern the qualitative and quantitative trajectories of quite a few deterministic, discrete dynamical structures, supplying resolution tools for platforms that may be solved analytically and strategies of qualitative research for structures that don't enable or necessitate an specific resolution.

The Third Option for the South China Sea: The Political Economy of Regional Conflict and Cooperation

This Palgrave Pivot makes use of an easy version from video game idea to provide an explanation for the habit of nations disputing possession of assets and of small islands within the South China Sea. It argues that the quick transformation of the region's financial system - the increase of manufacturing unit Asia – isn't being said, top nations to take possibilities past what a rational photo of prices and merits could recommend.

An Introduction to Complex Systems: Society, Ecology, and Nonlinear Dynamics

This undergraduate textual content explores numerous large-scale phenomena - worldwide warming, ice a long time, water, poverty - and makes use of those case experiences as a motivation to discover nonlinear dynamics, power-law information, and intricate platforms. even supposing the certain mathematical descriptions of those themes should be hard, the results of a process being nonlinear, power-law, or complicated are in truth relatively obtainable.

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

Sample text

The triplet (a, σ 2 , λL ) is called the generating triplet of the infinitely divisible characteristic function φ. 11. A distribution is infinitely divisible if and only if it is the weak limit of a sequence of distributions, each of which is compound Poisson (the reader may refer to Breiman (1968)). 12. We will say that two distribution functions F and G on R are of the same type if there exist two constants a ∈ R∗+ and b ∈ R such that F (ax + b) = G(x) for any x ∈ R. It is easy to see that this is an equivalence relation.

0, n i=1 f (yi ), if y1 < y2 < · · · < yn , otherwise. 18. Let X and (Yn )n∈N be random variables such that X ∼ E(1), Yn (ω) = n, if X(ω) ≤ n1 , 0, otherwise. Give, if it exists, the limit lim Yn : n→∞ • • • • in distribution, in probability, almost surely, in mean of order p ≥ 1. 19. Let (Xn )n∈N be a sequence of uncorrelated random variables with common expected value E[Xi ] = μ and such that sup V ar[Xi ] < +∞. Xi n Show that i=1 converges to μ in mean of order p = 2. 20. Give an example of random variables X, X1 , X2 , .

S. Proof: Let G ∈ G; then, by independence, Y dP = IG Y dP = E[IG Y ] = E[IG ]E[Y ] = P (G)E[Y ] = G E[Y ]dP, G from which the proposition follows. 122. Both the monotone and dominated convergence theorems extend in an analogous way to expectations conditional on σ-algebras. 123. A family of random variables (Yn )n∈N is uniformly integrable if lim sup m→∞ n |Yn |≥m |Yn |dP = 0. 124. Let (Yn )n∈N be a family of random variables in L1 . Then the following two statements are equivalent: 1. (Yn )n∈N is uniformly integrable, 2.

Download PDF sample

Download An Introduction to Continuous-Time Stochastic Processes: by Vincenzo Capasso, David Bakstein PDF
Rated 4.48 of 5 – based on 14 votes
[an error occurred while processing the directive]