Topic
Continuous-time stochastic process
About: Continuous-time stochastic process is a research topic. Over the lifetime, 5544 publications have been published within this topic receiving 216211 citations. The topic is also known as: continuous-space-time stochastic process.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this article, a method for making successive experiments at levels x1, x2, ··· in such a way that xn will tend to θ in probability is presented.
Abstract: Let M(x) denote the expected value at level x of the response to a certain experiment. M(x) is assumed to be a monotone function of x but is unknown to the experimenter, and it is desired to find the solution x = θ of the equation M(x) = α, where a is a given constant. We give a method for making successive experiments at levels x1, x2, ··· in such a way that xn will tend to θ in probability.
11,325 citations
Book•
20 Dec 1990TL;DR: In this article, a representation of stochastic processes and response statistics are represented by finite element method and response representation, respectively, and numerical examples are provided for each of them.
Abstract: Representation of stochastic processes stochastic finite element method - response representation stochastic finite element method - response statistics numerical examples.
6,624 citations
Book•
1 Jun 1992
TL;DR: In this article, a time-discrete approximation of deterministic Differential Equations is proposed for the stochastic calculus, based on Strong Taylor Expansions and Strong Taylor Approximations.
Abstract: 1 Probability and Statistics- 2 Probability and Stochastic Processes- 3 Ito Stochastic Calculus- 4 Stochastic Differential Equations- 5 Stochastic Taylor Expansions- 6 Modelling with Stochastic Differential Equations- 7 Applications of Stochastic Differential Equations- 8 Time Discrete Approximation of Deterministic Differential Equations- 9 Introduction to Stochastic Time Discrete Approximation- 10 Strong Taylor Approximations- 11 Explicit Strong Approximations- 12 Implicit Strong Approximations- 13 Selected Applications of Strong Approximations- 14 Weak Taylor Approximations- 15 Explicit and Implicit Weak Approximations- 16 Variance Reduction Methods- 17 Selected Applications of Weak Approximations- Solutions of Exercises- Bibliographical Notes
6,574 citations
Book•
1 Jan 1990
TL;DR: In this article, the authors propose a method for general stochastic integration and local times, which they call Stochastic Differential Equations (SDEs), and expand the expansion of Filtrations.
Abstract: I Preliminaries.- II Semimartingales and Stochastic Integrals.- III Semimartingales and Decomposable Processes.- IV General Stochastic Integration and Local Times.- V Stochastic Differential Equations.- VI Expansion of Filtrations.- References.
6,336 citations
TL;DR: This work represents the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error.
Abstract: We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error Several continuous and discrete processes are treated, and numerical examples show substantial speed-up compared to Monte Carlo simulations for low dimensional stochastic inputs
5,107 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 8 |
| 2024 | 11 |
| 2023 | 16 |
| 2022 | 33 |
| 2021 | 1 |
| 2020 | 2 |