Abstract
This chapter examines stochastic problems defined by
where n ≥ 1 is an integer, x and t denote space and time parameters, respectively, V can be an algebraic, differential, or integral operator with deterministic coefficients that may or may not depend on time, Y is the random input, and X denotes the output. It is common in applications to concentrate on values of X at a finite number of points X k ∈ D rather then all points of D. Systems described by the evolution in time of A’ at a finite number of points and at all points in D are called discrete and continuous respectively. The focus of this chapter is on discrete systems since they are used extensively in applications and are simpler to analyze than continuous systems. The vector X(t) ∈ ℝd collecting the processes X(xk, t), called the state vector defines the evolution of a discrete system. The mapping from Y to X can be with or without memory. An extensive discussion on memoryless transformations of random processes can be found in [79] (Chapters 3, 4, and 5) and is not presented here.
Keywords
- Deterministic System
- Moment Equation
- Error Covariance Matrix
- Compound Poisson Process
- European Call Option
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Grigoriu, M. (2002). Deterministic Systems and Stochastic Input. In: Stochastic Calculus. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8228-6_7
Download citation
DOI: https://doi.org/10.1007/978-0-8176-8228-6_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6501-6
Online ISBN: 978-0-8176-8228-6
eBook Packages: Springer Book Archive